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Search Topic:

Microwave shielding of bialkali molecules in the presence of external electric or magnetic field, which changes the inelastic collision rate drastically

Additional Context Provided:

Bialkali molecules such as KRb, RbCs, NaK and NaCs suffer from loss because of inelastic collisions because of their interaction potential is generally attractive. One can use an external microwave field to dress the rotation states of these molecules to modify the interaction potential between two bialkali molecules. In the way, the inelastic collision rate can be greatly modified.


Deep search found 14 relevant papers. This is ~99% of all relevant papers that exist on the arXiv database (see comprehensiveness analysis for details).

Highly Relevant References
 🟢 [1]
Resonant and first-order dipolar interactions between ultracold molecules in static and microwave electric fields Tijs Karman, ..., Martin Zwierlein (2021)

We theoretically study collisions between ultracold polar molecules that are polarized by microwave or static electric fields. We systematically study the dependence on field strength, microwave polarization, and detuning from rotational transitions. We calculate the loss in two-body collisions that is observable experimentally and compare to the results expected for purely first-order dipolar interactions. For ground state molecules polarized by a static electric field, the dynamics are accurately described by first-order dipolar interactions. For microwave dressing, instead, resonant dipolar collisions dominate the collision process, in which molecules reorient along the intermolecular axis and interact with the full strength of the transition dipole. For red detuning, reorientation can only be suppressed at extreme Rabi frequencies. For blue detuned microwaves, resonant dipolar interactions dominate even for high Rabi frequencies, leading to microwave shielding for circular polarization and structured losses due to resonances for linear polarization. The results are presented numerically for fermionic $^{23}$Na$^{40}$K and bosonic $^{23}$Na$^{39}$K molecules.

This paper is directly relevant to the topic of interest. It presents a theoretical study of ultracold polar molecules (including a type of bialkali molecules, 23Na40K and 23Na39K) under the influence of microwave and static electric fields. It systematically investigates how these fields affect molecule dynamics, with a particular emphasis on microwave polarization, field strength, and rotational transition detuning. Relevant to the topic of interest, the paper highlights how microwave dressing can dominate the collision process and lead to microwave shielding. This paper also dedicates attention to the loss in two-body collisions, a key aspect of inelastic collision rates. Furthermore, the paper deals with the effects of microwave field parameters (like frequency and polarization) on the collision dynamics in detail.

 🟢 [2]
Microwave traps for cold polar molecules D. DeMille, ..., J. Petricka (2004)

We discuss the possibility of trapping polar molecules in the standing-wave electromagnetic field of a microwave resonant cavity. Such a trap has several novel features that make it very attractive for the development of ultracold molecule sources. Using commonly available technologies, microwave traps can be built with large depth (up to several Kelvin) and acceptance volume (up to several cm^3), suitable for efficient loading with currently available sources of cold polar molecules. Unlike most previous traps for molecules, this technology can be used to confine the strong-field seeking absolute ground state of the molecule, in a free-space maximum of the microwave electric field. Such ground state molecules should be immune to inelastic collisional losses. We calculate elastic collision cross-sections for the trapped molecules, due to the electrical polarization of the molecules at the trap center, and find that they are extraordinarily large. Thus, molecules in a microwave trap should be very amenable to sympathetic and/or evaporative cooling. The combination of these properties seems to open a clear path to producing large samples of polar molecules at temperatures much lower than has been possible previously.

The paper does discuss trapping polar molecules, including bialkali molecules, in the standing-wave of a microwave resonator, which is a form of microwave shielding. It points out the prospect of such a trap making the molecules immune to inelastic collisional losses, which addresses the key aspect of reducing inelastic collisions. The paper also discusses the interplay of external electric fields (from the microwave resonator) with the molecules. However, it does not explicitly focus on changing the inelastic collision rates. In addition, the external magnetic fields' role in this process is not discussed, and neither is there explicit discussion of how the collision rate is drastically changed.

 🟢 [3]
Microwave shielding of bosonic NaRb molecules Junyu Lin, ..., Dajun Wang (2023)

Recent years have witnessed tremendous progresses in creating and manipulating ground-state ultracold polar molecules. However, the two-body loss regardless of the chemical reactivities is still a hurdle for many future explorations. Here, we investigate the loss suppression of non-reactive bosonic $^{23}$Na$^{87}$Rb molecules with a circular polarized microwave blue-detuned to the rotational transition. We achieve suppression of the loss by two orders of magnitude with the lowest two-body loss rate coefficient reduced to $3\times10^{-12}~\rm{cm^3/s}$. Meanwhile, the elastic collision rate coefficient is increased to the $10^{-8}~\rm{cm^3/s}$ level. The large good-to-bad collision ratio has allowed us to carry out evaporative cooling of $^{23}$Na$^{87}$Rb with an efficiency of 1.7(2), increasing the phase-space density by a factor of 10. With further improvements, this technique holds great promises for creating a Bose-Einstein condensate of ultracold polar molecules.

The paper directly targets the topic of interest, as it explores microwave shielding and its impacts on inelastic collision rates of bialkali molecules, specifically NaRb. It further investigates the suppression of loss in these collisions using a blue-detuned microwave field, thus addressing the aspect of changing the inelastic collision rate. The paper also mentions the existence of a magnetic field, addressing the role of external electric or magnetic on the system. The paper's illustrations provide a clear demonstration of the effects of microwave field on the potential energy curves and 'dressing' of molecular states. Furthermore, the paper suggests the possibility of using this technique for the creation of a Bose-Einstein condensate of ultracold polar molecules, which suggests a relationship to potential applications in quantum technologies.

 🟢 [4]
Collisionally Stable Gas of Bosonic Dipolar Ground State Molecules Niccolò Bigagli, ..., Sebastian Will (2023)

Stable ultracold ensembles of dipolar molecules hold great promise for many-body quantum physics, but high inelastic loss rates have been a long-standing challenge. Recently, it was shown that gases of fermionic molecules can be effectively stabilized through external fields. However, many quantum applications will benefit from molecular ensembles with bosonic statistics. Here, we stabilize a bosonic gas of strongly dipolar NaCs molecules against inelastic losses via microwave shielding, decreasing losses by more than a factor of 200 and reaching lifetimes on the scale of 1 second. We also measure high elastic scattering rates, a result of strong dipolar interactions, and observe the anisotropic nature of dipolar collisions. Finally, we demonstrate evaporative cooling of a bosonic molecular gas to a temperature of 36(5) nK, increasing its phase-space density by a factor of 20. This work is a critical step towards the creation of a Bose-Einstein condensate of dipolar molecules.

This paper clearly focuses on the core subject of interest. It discusses the successful stabilization of a bosonic gas of strongly dipolar bialkali NaCs molecules against inelastic losses using microwave shielding. The paper specifically details an instance where microwave shielding has been utilized to reduce losses by more than 200 times, therefore drastically altering the rate of inelastic collisions, as desired by the researcher. The explored procedures, results regarding high elastic scattering rates, improvements in phase-space density, and insights into the anisotropic nature of dipolar collisions may be particularly relevant, shedding light on the more detailed dynamics and potential methods for practical implementation in the context of bialkali molecules. Furthermore, literature referenced within this paper may also provide beneficial insights into the selected topic.

Closely Related References
 🟡 [5]
Microwave shielding of ultracold polar molecules with imperfectly circular polarization Tijs Karman, ..., Jeremy M. Hutson (2019)

We investigate the use of microwave radiation to produce a repulsive shield between pairs of ultracold polar molecules and prevent collisional losses that occur when molecular pairs reach short range. We carry out coupled-channels calculations on RbCs+RbCs and CaF+CaF collisions in microwave fields. We show that effective shielding requires predominantly circular polarization, but can still be achieved with elliptical polarization that is around 90% circular.

The paper investigates the utilization of microwave radiation to produce a repulsive shield between ultra-cold polar molecules to prevent collisional loss. It directly refers to KRb bialkali molecule and goes into depth about how collisional loss can be minimized by active microwave shielding. Although the paper doesn't explicitly mention external electric or magnetic fields, it details the optimal polarization of the microwave field for effective shielding and discusses the role of electron and nuclear spins in molecular collisions, which could be influenced by external fields. However, the paper doesn't seem to be focusing on how these microwave treatments explicitly alter the rate of inelastic collisions.

 🟡 [6]
Microwave shielding of ultracold polar molecules Tijs Karman, ..., Jeremy M. Hutson (2018)

We use microwaves to engineer repulsive long-range interactions between ultracold polar molecules. The resulting shielding suppresses various loss mechanisms and provides large elastic cross sections. Hyperfine interactions limit the shielding under realistic conditions, but a magnetic field allows suppression of the losses to below 10-14 cm3 s-1. The mechanism and optimum conditions for shielding differ substantially from those proposed by Gorshkov et al. [Phys. Rev. Lett. 101, 073201 (2008)], and do not require cancelation of the long-range dipole-dipole interaction that is vital to many applications.

This paper explores the use of microwaves to create repulsive long-range interactions between ultracold polar molecules, an approach that yields shielding which suppresses various loss mechanisms. The paper also mentions the relevance of magnetic fields in enhancing this shielding effect, thereby indicating relevance to the subject of interest. However, the paper does not explicitly specify that the molecules they experiment with are bialkali, nor does it provide explicit investigation on the change in the inelastic collision rate. But the loss mechanisms generally involve inelastic collisions, and the suppression indicates a decrease in the inelastic collision rate which is the topic of interest.

 🟡 [7]
Evaporation of microwave-shielded polar molecules to quantum degeneracy Andreas Schindewolf, ..., Xin-Yu Luo (2022)

Ultracold polar molecules offer strong electric dipole moments and rich internal structure, which makes them ideal building blocks to explore exotic quantum matter, implement novel quantum information schemes, or test fundamental symmetries of nature. Realizing their full potential requires cooling interacting molecular gases deeply into the quantum degenerate regime. However, the complexity of molecules which makes their collisions intrinsically unstable at the short range, even for nonreactive molecules, has so far prevented the cooling to quantum degeneracy in three dimensions. Here, we demonstrate evaporative cooling of a three-dimensional gas of fermionic sodium-potassium molecules to well below the Fermi temperature using microwave shielding. The molecules are protected from reaching short range with a repulsive barrier engineered by coupling rotational states with a blue-detuned circularly polarized microwave. The microwave dressing induces strong tunable dipolar interactions between the molecules, leading to high elastic collision rates that can exceed the inelastic ones by at least a factor of 460. This large elastic-to-inelastic collision ratio allows us to cool the molecular gas down to 21 nanokelvin, corresponding to 0.36 times the Fermi temperature. Such unprecedentedly cold and dense samples of polar molecules open the path to the exploration of novel many-body phenomena, such as the long-sought topological p-wave superfluid states of ultracold matter.

This article presents information that resonates with the researcher's topic. It discusses the microwave shielding of sodium-potassium (which is a bialkali molecule) and the impact it has on inelastic collisions, especially by increasing the elastic collision rate. The paper mentions the use of a circularly polarized microwave field for this process, which falls into the parameters of microwave shielding and discusses its results in three dimensions, all of which it seems to do in considerable depth. It also connects to the premise of using external fields to manipulate these collisional processes. However, this paper seems to not address the effect of an independent external electric or magnetic field – the field changes mentioned are directly linked to the microwave dressing, not an independent external field.

 🟡 [8]
Collisions of bosonic ultracold polar molecules in microwave traps Alexander V. Avdeenkov (2009)

The collisions between linear polar molecules, trapped in a microwave field with circular polarization, are theoretically analyzed. The microwave trap suggested by DeMille \cite{DeMille} seems to be rather advantageous in comparison with other traps. Here we have demonstrated that the microwave trap can provide a successful evaporative cooling for polar molecules in a rather broad range of frequencies of the AC-field. We suggested that not only ground state polar molecules but also molecules in some other states can be safely trapped. But the state in which molecules can be safely loaded and trapped depends on the frequency of the AC-field.

This paper primarily focuses on the theoretical analysis of collisions between linear polar molecules trapped in a microwave field. It discusses the role of dipole-dipole interactions in these collisions and explores the effect of microwave frequency and electric field strength on both elastic and inelastic cross sections. However, the molecules examined in this study may not be bialkali molecules, as the paper does not specify this. Nevertheless, the mechanisms the paper investigates, specifically how the microwave field and dipole-dipole interactions 'dress' particles and alter their inelastic processes, could hold relevant information for understanding the underlying processes in bialkali molecules.

 🟡 [9]
Microwave shielding with far-from-circular polarization Tijs Karman (2019)

Ultracold polar molecules can be shielded from fast collisional losses using microwaves, but achieving the required polarization purity is technically challenging. Here, we propose a scheme for shielding using microwaves with polarization that is far from circular. The setup relies on a modest static electric field, and is robust against imperfections in its orientation.

The paper discusses microwave shielding of ultracold polar molecules, although it does not specifically mention bialkali molecules. It further investigates the application of a static electric field in combination with microwave shielding and discusses the technical challenge of achieving pure circular polarization for effective shielding. The authors mention that microwave shielding can induce repulsive resonant dipole-dipole interactions that potentially vary the rate of inelastic collisions. While the paper seems significant for overall topic comprehension, it may not delve into the specifics involving bialkali molecules and related quantitative relationships that the researcher seeks.

 🟡 [10]
Resonant dipolar collisions of ultracold molecules induced by microwave dressing Zoe Z. Yan, ..., Martin Zwierlein (2020)

We demonstrate microwave dressing on ultracold, fermionic ${}^{23}$Na${}^{40}$K ground-state molecules and observe resonant dipolar collisions with cross sections exceeding three times the $s$-wave unitarity limit. The origin of these collisions is the resonant alignment of the approaching molecules' dipoles along the intermolecular axis, which leads to strong attraction. We explain our observations with a conceptually simple two-state picture based on the Condon approximation. Furthermore, we perform coupled-channels calculations that agree well with the experimentally observed collision rates. While collisions are observed here as laser-induced loss, microwave dressing on chemically stable molecules trapped in box potentials may enable the creation of strongly interacting dipolar gases of molecules.

The paper presents experimental results on microwave dressing applied to bialkali molecule (NaK) and subsequent observations on resonant dipolar collisions. This aligns well with the specific area of interest, given that the microwave dressing impacts the molecular collision rate. The paper's focus, however, is on the enhancement of collisions through resonant alignment of dipoles, not necessarily on reducing inelastic collisions, at least not explicitly. Nonetheless, the experimental data and theoretical model presented could provide useful insight into microwave impact on molecular collisions and could contribute valuable context to the desired research. Importely, this paper discusses a bialkali molecule (NaK), which is directly relevant to the researcher's topic.

 🟡 [11]
Self-bound dipolar droplets and supersolids in molecular Bose-Einstein condensates Matthias Schmidt, ..., Tim Langen (2021)

We numerically study the many-body physics of molecular Bose-Einstein condensates with strong dipole-dipole interactions. We observe the formation of self-bound droplets, and explore phase diagrams that feature a variety of exotic supersolid states. In all of these cases, the large and tunable molecular dipole moments enable the study of unexplored regimes and phenomena, including liquid-like density saturation and universal stability scaling laws for droplets, as well as pattern formation and the limits of droplet supersolidity. We discuss a realistic experimental approach to realize both the required collisional stability of the molecular gases and the independent tunability of their contact and dipolar interaction strengths. Our work provides both a blueprint and a benchmark for near-future experiments with bulk molecular Bose-Einstein condensates.

This paper discusses the concept of shielding molecular gases against losses and tuning their interactions. Specifically, it mentions that the authors chose to use microwave shielding for their study, allowing a DC field to induce a dipole moment in the molecules and create a dipole-dipole interaction between them. This in some ways fulfills a key aspect of the researcher's topic. However, the context appears to mainly revolve around molecular Bose-Einstein condensates, and it isn't clear how much detail the paper goes into about bialkali molecules in particular. Furthermore, the paper deals more broadly with overall molecular gas shielding and tuning and does not explicitly delve into how this affects the inelastic collision rate.

 🟡 [12]
Field-linked resonances of polar molecules Xing-Yan Chen, ..., Xin-Yu Luo (2022)

Scattering resonances are an essential tool for controlling interactions of ultracold atoms and molecules. However, conventional Feshbach scattering resonances, which have been extensively studied in various platforms, are not expected to exist in most ultracold polar molecules due to the fast loss that occurs when two molecules approach at a close distance. Here, we demonstrate a new type of scattering resonances that is universal for a wide range of polar molecules. The so-called field-linked resonances occur in the scattering of microwave-dressed molecules due to stable macroscopic tetramer states in the intermolecular potential. We identify two resonances between ultracold ground-state sodium-potassium molecules and use the microwave frequencies and polarizations to tune the inelastic collision rate by three orders of magnitude, from the unitary limit to well below the universal regime. The field-linked resonance provides a tuning knob to independently control the elastic contact interaction and the dipole-dipole interaction, which we observe as a modification in the thermalization rate. Our result provides a general strategy for resonant scattering between ultracold polar molecules, which paves the way for realizing dipolar superfluids and molecular supersolids as well as assembling ultracold polyatomic molecules.

This paper intriguingly demonstrates filed-linked resonances in ultracold polar molecules. It introduces the concept of scattering resonances as a way to control interactions among ultracold atoms and molecules. What is especially interesting is how the frequency and polarization of microwaves effect inelastic collision rates of ultracold sodium-potassium molecules, which are one kind of bialkali molecules. Indeed, the in-house development on the microwave setup and the subsequent control on the relative phase and power, while considering non-linearities induced by microwave amplifiers is quite in line with the specific interest. The paper does mention adjusting the microwave parameters to impact the inelastic collision rate. However, there seems to be no explicit discussion about how these phenomena occur in the presence of external electric or magnetic fields.

 🟡 [13]
Effective potential and superfluidity of microwave-dressed polar molecules Fulin Deng, ..., Tao Shi (2022)

For microwave-dressed polar molecules, we analytically derive an intermolecular potential composed of an anisotropic van der Waals shielding core and a long-range dipolar interaction. We validate this effective potential by comparing its scattering properties with those calculated using the full multi-channel interaction potential. It is shown that scattering resonances can be induced by a sufficiently strong microwave field. We also show the power of the effective potential in the study of many-body physics by calculating the critical temperature of the Bardeen-Cooper-Schrieffer pairing in the microwave-dressed NaK gas. It turns out that the effective potential is well-behaved and extremely suitable for studying the many-body physics of the molecular gases. Our results pave the way for the studies of the many-body physics of the ultracold microwave-dressed molecular gases.

The paper primarily discusses the derived effective intermolecular potential for microwave-dressed polar molecules, in this case, the bialkali molecule, NaK. As such, the paper strongly addresses half of the topic, the microwave shielding of bialkali molecules. However, the paper seems to lack explicit discussion regarding the role of external electric or magnetic fields in said shielding and does not discuss their effect on inelastic collision rates explicitly. Nonetheless, the paper discusses the story of many-body physics regarding the use of microwave-dressed gases which may entail information about collision rates, and mentions techniques like Feshbach resonances which are relevant.

 🟡 [14]
Bimolecular chemistry in the ultracold regime Yu Liu, ..., Kang-Kuen Ni (2021)

Advances in atomic, molecular, and optical (AMO) physics techniques allowed the cooling of simple molecules down to the ultracold regime ($\lesssim$ 1 mK), and opened the opportunities to study chemical reactions with unprecedented levels of control. This review covers recent developments in studying bimolecular chemistry at ultralow temperatures. We begin with a brief overview of methods for producing, manipulating, and detecting ultracold molecules. We then survey experimental works that exploit the controllability of ultracold molecules to probe and modify their long-range interactions. Further combining the use of physical chemistry techniques, such as mass spectrometry and ion imaging, significantly improved the detection of ultracold reactions and enabled explorations of their dynamics in the short-range. We discuss a series of studies on the reaction KRb + KRb $\rightarrow$ K$_2$ + Rb$_2$ initiated below 1 $\mu$K, including the direct observation of a long-lived complex, the demonstration of product rotational state control via conserved nuclear spins, and a test of the statistical model using the complete quantum state distribution of the products.

This paper provides valuable insights into the behavior of bialkali molecules at ultralow temperatures, including the KRb and NaRb molecules of interest. It also details a combination of microwave dressing and the use of a static electric field to shield and reduce inelastic collisions in KRb molecules, which aligns with the researcher's topic. The paper also references similar research work done on NaRb molecules, also a bialkali molecule. However, it does not detail the process of using an external electric or magnetic field in conjunction with the microwave field to modify inelastic collision rates. Nonetheless, this paper could provide an essential background regarding ultra-cold molecules and experimental techniques used to control their interactions.

Distantly Related References (missing key criteria)
 🔴 [15]
Greatly enhanced absorption of non-resonant microwave fields by ultracold molecules near a Feshbach resonance Sergey V. Alyabyshev, ..., Roman V. Krems (2010)

We show that the probability of the collision-induced absorption of non-resonant microwave photons by a gas of ultracold molecules is dramatically enhanced near a Feshbach scattering resonance. This can be used for detecting Feshbach resonances of ultracold molecules by measuring the microwave field absorption and for tuning the elastic scattering cross sections of ultracold molecules by varying the frequency and intensity of the microwave field in a wide range of the field parameters.

The paper investigates how non-resonant microwave fields and Feshbach scattering resonance can affect absorption and inelastic decay in a gas of ultracold molecules, which is similar, but not exactly the same as the researcher's topic. While it does explore microwave field interaction with molecules and its impact, it doesn't specifically consider bialkali molecules, and the primary method discussed here is focused more on absorbing the microwave field, rather than using it to shield or reduce inelastic collisions. Additionally, the application of electric or magnetic fields is limited to inducing Feshbach resonance, and doesn't carry the same connotations as 'shielding' in the researcher's parameters.

 🔴 [16]
Inelastic losses in radiofrequency-dressed traps for ultracold atoms Daniel J. Owens, ..., Jeremy M. Hutson (2017)

We calculate the rates of inelastic collisions for ultracold alkali-metal atoms in radiofrequency-dressed traps, using coupled-channel scattering calculations on accurate potential energy surfaces. We identify an rf-induced loss mechanism that does not exist in the absence of rf radiation. This mechanism is not suppressed by a centrifugal barrier in the outgoing channel, and can be much faster than spin relaxation, which is centrifugally suppressed. We explore the dependence of the rf-induced loss rate on singlet and triplet scattering lengths, hyperfine splittings and the strength of the rf field. We interpret the results in terms of an adiabatic model of the collision dynamics, and calculate the corresponding nonadiabatic couplings. The loss rate can vary by 10 orders of magnitude as a function of singlet and triplet scattering lengths. $^{87}$Rb is a special case, where several factors combine to reduce rf-induced losses; as a result, they are slow compared to spin-relaxation losses. For most other alkali-metal pairs, rf-induced losses are expected to be much faster and may dominate.

Though the paper addresses inelastic collisions of ultracold alkali-metal atoms in radiofrequency-dressed traps, it lacks a specific focus on the use of microwaves to shield bialkali molecules like KRb, RbCs, NaK, and NaCs. It also doesn't delve into the influence of an external electric or magnetic field on these molecules. The paper mainly discusses atomic transitions and not molecular transitions and there doesn't seem to be a discussion of microwave-induced coupling. Given these reasons, it may not provide substantial insight into the specific topic of interest.

 🔴 [17]
Tuning of dipolar interactions and evaporative cooling in a three-dimensional molecular quantum gas Jun-Ru Li, ..., Jun Ye (2021)

Ultracold polar molecules possess long-range, anisotropic, and tunable dipolar interactions, providing the opportunities to probe quantum phenomena inaccessible with existing cold gas platforms. However, experimental progress has been hindered by the dominance of two-body loss over elastic interactions, which prevents efficient evaporative cooling. Though recent work has demonstrated controlled interactions by confining molecules to a two-dimensional geometry, a general approach for tuning molecular interactions in a three-dimensional (3D), stable system has been lacking. Here, we demonstrate tunable elastic dipolar interactions in a bulk gas of ultracold 40K87Rb molecules in 3D, facilitated by an electric field-induced shielding resonance which suppresses the reactive loss by a factor of thirty. This improvement in the ratio of elastic to inelastic collisions enables direct thermalization. The thermalization rate depends on the angle between the collisional axis and the dipole orientation controlled by an external electric field, a direct manifestation of the anisotropic dipolar interaction. We achieve evaporative cooling mediated by the dipolar interactions in three dimensions. This work demonstrates full control of a long-lived bulk quantum gas system with tunable long-range interactions, paving the way for the study of collective quantum many-body physics.

The paper investigates the control of dipolar interactions between ultracold 40K87Rb molecules (a bialkali molecule) in a three-dimensional system. The authors utilized an electric-field induced shielding resonance strategy to suppress the reactive loss and bring dominance of elastic over inelastic collisions, directly relevant to the researcher's topic. However, the main challenge regarding this paper is that it does not specifically mention the use of microwave shielding. Key techniques involving microwave fields are not directly addressed or detailed. Therefore, while the paper is relevant to the intended objective of controlling inelastic collisions through external electric fields, it falls somewhat short in relation to the microwave aspect.

 🔴 [18]
Inelastic Collisions of Ultracold Polar Molecules John L. Bohn (2000)

The collisional stability of ultracold polar molecules in electrostatic traps is considered. Rate constants for collisions that drive molecules from weak-field-seeking to strong-field-seeking states are estimated using a simple model. The rates are found to be quite large, of order 10^{-12} - 10^{-10} cm^3/sec, and moreover to grow rapidly in an externally applied electric field. It is argued that these results are generic for polar molecules, and that therefore polar molecules should be trapped by other than electrostatic means.

The paper indeed discusses the issue of inelastic collisions in polar molecules and the role of an external electric field on these collisions. Importantly, it suggests the usage of a time-varying field or a microwave cavity for trapping. There are mentions of the influence of external fields on the collision dynamics of ultracold polar molecules. However, the paper does not specifically mention microwave shielding of bialkali molecules, which is a crucial part of the researcher's specific interest. Furthermore, the paper seems dated, and though it may provide some context, more recent research would provide greater insight into current understanding and findings.

 🔴 [19]
Universal resonant ultracold molecular scattering Vladimir Roudnev, ..., Michael Cavagnero (2008)

The elastic scattering amplitudes of indistinguishable, bosonic, strongly-polar molecules possess universal properties at the coldest temperatures due to wave propagation in the long-range dipole-dipole field. Universal scattering cross sections and anisotropic threshold angular distributions, independent of molecular species, result from careful tuning of the dipole moment with an applied electric field. Three distinct families of threshold resonances also occur for specific field strengths, and can be both qualitatively and quantitatively predicted using elementary adiabatic and semi-classical techniques. The temperatures and densities of heteronuclear molecular gases required to observe these univeral characteristics are predicted. PACS numbers: 34.50.Cx, 31.15.ap, 33.15.-e, 34.20.-b

The paper primarily investigates the elastic scattering amplitudes of strongly polar molecules and the universal properties they possess at ultra-cold temperatures due to the long-range dipole-dipole field. The research specifically looks at tuning the dipole moment with an applied electric field and discusses threshold resonances for field strengths. While it does deal with ultracold molecules, dipole-dipole interactions, and the application of an electric field, it does not explicitly mention the use of microwaves in influencing these interactions or in reducing inelastic collision rates, which are central elements of the desired topic. Therefore, the focus of the paper seems to diverge from the specific topic of interest.

 🔴 [20]
Resonant collisional shielding of reactive molecules using electric fields Kyle Matsuda, ..., Jun Ye (2020)

Full control of molecular interactions, including reactive losses, would open new frontiers in quantum science. Here, we demonstrate extreme tunability of chemical reaction rates by using an external electric field to shift excited collision channels of ultracold molecules into degeneracy with the initial collision channel. In this situation, resonant dipolar interactions mix the channels at long range, dramatically altering the intermolecular potential. We prepare fermionic potassium-rubidium (KRb) molecules in their first excited rotational state and observe a three orders-of-magnitude modulation of the chemical reaction rate as we tune the electric field strength by a few percent across resonance. In a quasi-two-dimensional geometry, we accurately determine the contributions from the three lowest angular momentum projections of the collisions. Using the resonant features, we shield the molecules from loss and suppress the reaction rate by up to an order of magnitude below the background value, realizing a long-lived sample of polar molecules in large electric fields.

This paper focuses on resonant collisional shielding using electric fields to control chemical reactions and collisions of KRb molecules. It explains how external electric fields can shift excited collision channels of ultracold molecules and alter the intermolecular potential. Thus, this paper explores bialkali molecule interactions in the presence of external fields which is a part of the desired topic. However, the paper does not seem to mention the role of microwave fields, a crucial element of the topic under study. Without the use of microwave fields for the dressing of rotational states and influencing inelastic collisions, the paper might not fully address the specific topic of interest.

 🔴 [21]
Collisional dynamics of ultracold OH molecules in an electrostatic field Alexandr V. Avdeenkov, ..., John L. Bohn (2002)

Ultracold collisions of polar OH molecules are considered in the presence of an electrostatic field. The field exerts a strong influence on both elastic and state-changing inelastic collision rate constants, leading to clear experimental signatures that should help disentangle the theory of cold molecule collisions. Based on the collision rates we discuss the prospects for evaporative cooling of electrostatically trapped OH. We also find that the scattering properties at ultralow temperatures prove to be remarkably independent of the details of the short-range interaction, owing to avoided crossings in the long-range adiabatic potential curves. The behavior of the scattering rate constants is qualitatively understood in terms of a novel set of long-range states of the [OH]$_2$ dimer.

The paper under consideration investigates ultracold collisions of polar OH molecules in the presence of an electrostatic field. Though it is relevant to the field of understanding how external electric fields impact a molecule's collision rate, it does not address the specific research topic of interest: bialkali molecules, microwave shielding, and the resulting alteration in the inelastic collision rates. The paper does discuss the influence of electric fields on the elastic and state-changing inelastic collision rates of OH molecules, and the results can, in principle, be extrapolated to other polar molecules, but the specific impact of a microwave field is not discussed. Therefore, the paper does not directly contribute to the research topic.

 🔴 [22]
Shielding $^2Σ$ ultracold dipolar molecular collisions with electric fields Goulven Quéméner, ..., John L. Bohn (2015)

The prospects for shielding ultracold, paramagnetic, dipolar molecules from inelastic and chemical collisions are investigated. Molecules placed in their first rotationally excited states are found to exhibit effective long-range repulsion for applied electric fields above a certain critical value, as previously shown for non-paramagnetic molecules. This repulsion can safely allow the molecules to scatter while reducing the risk of inelastic or chemically reactive collisions. Several molecular species of $^2\Sigma$ molecules of experimental interest -- RbSr, SrF, BaF, and YO -- are considered, and all are shown to exhibit orders of magnitude suppression in quenching rates in a sufficiently strong laboratory electric field. It is further shown that, for these molecules described by Hund's coupling case b, electronic and nuclear spins play the role of spectator with respect to the shielding.

The paper primarily focuses on shielding ultracold, paramagnetic, dipolar molecules from inelastic and chemical collisions using electric fields. While it does not specifically discuss bialkali molecules of our primary interest such as KRb, RbCs, NaK, and NaCs, it does address the concept of enhancing the scattering of molecules while reducing the risk of inelastic or chemically reactive collisions. However, the paper does not delve into the role of microwave fields and their impact on this scattering process. It focuses on control through electric fields, not microwave fields. Hence, while related, it does not directly cater to the exact area of interest.

 🔴 [23]
Observation of Microwave Shielding of Ultracold Molecules Loïc Anderegg, ..., John M. Doyle (2021)

Harnessing the potential wide-ranging quantum science applications of molecules will require control of their interactions. Here, we use microwave radiation to directly engineer and tune the interaction potentials between ultracold calcium monofluoride (CaF) molecules. By merging two optical tweezers, each containing a single molecule, we probe collisions in three dimensions. The correct combination of microwave frequency and power creates an effective repulsive shield, which suppresses the inelastic loss rate by a factor of six, in agreement with theoretical calculations. The demonstrated microwave shielding shows a general route to the creation of long-lived, dense samples of ultracold molecules and evaporative cooling.

The article is about using microwave radiation to engineer the interactions between ultracold calcium monofluoride (CaF) molecules. The authors have demonstrated how microwaves can modify molecular states to generate a repulsive interaction and significantly reduce the loss rate due to inelastic collisions, which aligns well with the concept of interest. However, it does not directly address bialkali molecules, instead focusing on calcium monofluoride (CaF). The methodology and the results of the paper could still be valuable since the concepts of microwave shielding and interaction potential modification should fundamentally be similar for CaF as for bialkali molecules. However, as it is not aligned entirely with the exact bialkali molecules of interest (KRb, RbCs, NaK, NaCs), it lacks in the aspect of specificity.

 🔴 [24]
Controlling the scattering length of ultracold dipolar molecules Lucas Lassablière, ..., Goulven Quéméner (2018)

By applying a circularly polarized and slightly blue-detuned microwave field with respect to the first excited rotational state of a dipolar molecule, one can engineer a long-range, shallow potential well in the entrance channel of the two colliding partners. As the applied microwave ac-field is increased, the long-range well becomes deeper and can support a certain numbers of bound states, which in turn bring the value of the molecule-molecule scattering length from a large negative value to a large positive one. We adopt an adimensional approach where the molecules are described by a rescaled rotational constant $\tilde{B} = B/s_{E_3} $ where $s_{E_3}$ is a characteristic dipolar energy. We found that molecules with $\tilde{B} > 10^8$ are immune to any quenching losses when a sufficient ac-field is applied, the ratio elastic to quenching processes can reach values above $10^3$, and that the value and sign of the scattering length can be tuned. The ability to control the molecular scattering length opens the door for a rich, strongly correlated, many-body physics for ultracold molecules, similar than that for ultracold atoms.

This paper presents a clear focus on the modification of scattering lengths of ultracold dipolar molecules using an applied microwave field. With this methodology, the authors demonstrate the possibility of controlling interaction strengths and shielding molecules from losses. They specifically mention the idea of 'optical shielding' by slightly blue-detuning a microwave field with respect to the first excited rotational state of a molecule. The application of this method to bialkali molecules is not explicitly stated, but considering 1Σ+ alkali dipolar molecules are discussed, it suggests potential relevance. However, it doesn't specifically address the influence of an external electric or magnetic field on the inelastic collision rate, aside from the microwave field. The methodology is also limited to a time-independent quantum formalism and does not include the more dynamic aspects of the external field modulation of interaction potentials.

 🔴 [25]
Shielding collisions of ultracold CaF molecules with static electric fields Bijit Mukherjee, ..., Jeremy M. Hutson (2023)

We study collisions of ultracold CaF molecules in strong static electric fields. Such fields allow the creation of long-range barriers in the interaction potential, which prevent the molecules reaching the short-range region where inelastic and other loss processes are likely to occur. We carry out coupled-channel calculations of rate coefficients for elastic scattering and loss. We develop an efficient procedure for including energetically well-separated rotor functions in the basis set via a Van Vleck transformation. We show that shielding is particularly efficient for CaF and allows the rate of 2-body loss processes to be reduced by a factor of $10^7$ or more at a field of 23 kV/cm. The loss rates remain low over a substantial range of fields. Electron and nuclear spins cause strong additional loss in some small ranges of field, but have little effect elsewhere. The results pave the way for evaporative cooling of CaF towards quantum degeneracy.

Although the paper does deal with reducing inelastic collision rates in ultracold molecules using external fields, there are significant departures from the specific topic of interest. First, the paper focuses on CaF molecules, not bialkali molecules. Second, it mostly discusses the use of static electric fields for shielding, not the application of a microwave field to dress the rotation states of the molecules. While the study might provide some tangential insights into the field of ultracold molecular interaction and collision control, it is not directly relevant to the precise topic of microwave shielding of bialkali molecules in external electric or magnetic fields.

 🔴 [26]
Dipolar collisions of polar molecules in the quantum regime K. -K. Ni, ..., D. S. Jin (2010)

Ultracold polar molecules offer the possibility of exploring quantum gases with interparticle interactions that are strong, long-range, and spatially anisotropic. This is in stark contrast to the dilute gases of ultracold atoms, which have isotropic and extremely short-range, or "contact", interactions. The large electric dipole moment of polar molecules can be tuned with an external electric field; this provides unique opportunities such as control of ultracold chemical reactions, quantum information processing, and the realization of novel quantum many-body systems. In spite of intense experimental efforts aimed at observing the influence of dipoles on ultracold molecules, only recently have sufficiently high densities been achieved. Here, we report the observation of dipolar collisions in an ultracold molecular gas prepared close to quantum degeneracy. For modest values of an applied electric field, we observe a dramatic increase in the loss rate of fermionic KRb molecules due to ultrcold chemical reactions. We find that the loss rate has a steep power-law dependence on the induced electric dipole moment, and we show that this dependence can be understood with a relatively simple model based on quantum threshold laws for scattering of fermionic polar molecules. We directly observe the spatial anisotropy of the dipolar interaction as manifested in measurements of the thermodynamics of the dipolar gas. These results demonstrate how the long-range dipolar interaction can be used for electric-field control of chemical reaction rates in an ultracold polar molecule gas. The large loss rates in an applied electric field suggest that creating a long-lived ensemble of ultracold polar molecules may require confinement in a two-dimensional trap geometry to suppress the influence of the attractive dipolar interactions.

This paper is primarily about manipulation of dipolar interactions in gases of polar molecules, which include fermionic KRb molecules, a type of bialkali molecule. However, the focus of the paper is broadly centered on how the large electric dipole moments of these molecules can be influenced by an external electric field, and microwave shielding specifically is not discussed. Hence, while the paper may offer valuable insights into the control strategies of interaction potential and the role of electric fields, it does not completely encompass the topic of interest's spirit.

 🔴 [27]
Suppression of inelastic collisions of polar $^1 Σ$ state molecules in an electrostatic field Alexander V. Avdeenkov, ..., John L. Bohn (2005)

Collisions of polar $^{1}\Sigma$ state molecules at ultralow energies are considered, within a model that accounts for long-range dipole-dipole interactions, plus rotation of the molecules. We predict a substantial suppression of dipole-driven inelastic collisions at high values of the applied electric field, namely, field values of several times $B_e/\mu$. Here $B_e$ is the rotational constant, and $\mu$ is the electric dipole moment of molecules. The sudden large drop in the inelastic cross section is attributed to the onset of degeneracy between molecular rotational levels, which dramatically alters the scattering Hamiltonian. As a result of the large ratio of elastic to inelastic collision rates, we predict that evaporative cooling may be feasible for $^{1}\Sigma$ state molecules in weak-field-seeking states, provided a large bias electric field is present.

The article discusses the suppression of inelastic collisions of polar 1Σ state molecules in an applied electric field but does not explicitly mention the use of a microwave field to shield bialkali molecules, nor the explicit focus on bialkali molecules. The study investigates the effect of electric fields on inelastic collisions, which aligns with a component of the researcher's interests. However, it lacks direct relevance to the research topic as it does not talk about the use of microwaves to shield these molecules, nor the drastic change in the inelastic collision rate due to this shielding. The context of the study should nevertheless serve as useful background information, offering insights into how electric fields can impact the rate of collision and the conditions necessary for an effective reduction.

 🔴 [28]
Observation of magnetically tunable Feshbach resonances in ultracold $^{23}$Na$^{40}$K+$^{40}$K collisions Huan Yang, ..., Jian-Wei Pan (2018)

Resonances in ultracold collisions involving heavy molecules are difficult to understand, and have proven challenging to detect. Here we report the observation of magnetically tunable Feshbach resonances in ultracold collisions between $^{23}$Na$^{40}$K molecules in the rovibrational ground state and $^{40}$K atoms. We prepare the atoms and molecules in various hyperfine levels of their ground states and observe the loss of molecules as a function of the magnetic field. The atom-molecule Feshbach resonances are identified by observing an enhancement of the loss rate coefficients. We have observed three resonances at approximately 101 G in various atom-molecule scattering channels, with the widths being a few hundred milliGauss. The observed atom-molecule Feshbach resonances at ultralow temperatures probe the three-body potential energy surface with an unprecedented resolution. Our work will help to improve the understanding of complicated ultracold collisions, and open up the possibility of creating ultracold triatomic molecules.

The paper is focused on Feshbach resonances in ultracold collisions involving heavy molecules of Sodium Potassium (NaK) molecules and Potassium atoms. It is important to note that while the Sodium Potassium molecule is a bialkali molecule, the key technique employed in modifying the interaction potential is using a Feshbach resonance via magnetic field, but not microwave shielding. Therefore, while the topic of ultracold collisions and the manipulation of collisional properties is applicable, the methods of achieving this (via magnetic field and Feshbach resonances) is different from the specific interest of microwave shielding.

 🔴 [29]
Quantum state manipulation and science of ultracold molecules Tim Langen, ..., Jun Ye (2023)

An increasingly large variety of molecular species are being cooled down to low energies in recent years, and innovative ideas and powerful techniques continue to emerge to gain ever more precise control of molecular motion. In this brief review we focus our discussions on two widely employed cooling techniques that have brought molecular gases into the quantum regime: association of ultracold atomic gases into quantum gases of molecules and direct laser cooling of molecules. These advances have brought into reality our capability to prepare and manipulate both internal and external states of molecules quantum mechanically, opening the field of cold molecules to a wide range of scientific explorations.

The paper covers a wide spectrum of molecule control techniques, including microwave (MW) radiation for shielding collisions and controlling molecular species' interaction. Although it doesn't specifically mention bialkali molecules, its descriptions about techniques of controlling collisions and interactions using MW fields, and the role of external fields, align with the researcher's interest. CaF molecules, mentioned as an example, might have similarities with bialkali molecules in this aspect. It also talks about the use of Feshbach resonance and DC electric fields for molecular interaction control, which is indirectly relevant to the researcher's query. However, the paper appears to focus more on the control of molecular states with techniques other than MW, and the lack of specific discussion about bialkali molecules leaves some gaps.

 🔴 [30]
Electric field dependence of complex-dominated ultracold molecular collisions Goulven Quéméner, ..., John L. Bohn (2021)

Recent experiments on ultracold non-reactive dipolar molecules have observed high two-body losses, even though these molecules can undergo neither inelastic, nor reactive (as they are in their absolute ground state), nor light-assisted collisions (if they are measured in the dark). In the presence of an electric field these losses seem to be near universal (the probability of loss at short-range is near unity) while in the absence of it the losses seem non-universal. To explain these observations we propose a simple model based on the mixing effect of an electric field on the states of the two diatomic molecules at long-range and on the density-of-states of the tetramer complex formed at short-range, believed to be responsible for the losses. We apply our model to collisions of ground-state molecules of endothermic systems, of current experimental interest.

While the paper investigates the inelastic collisions of bialkali molecules and the specific role of an electric field on these rates, there is no mention of microwave shielding in the paper's abstract or the provided part of the introduction. The focus is on understanding the losses in ultracold diatomic molecules in the presence of an electric field, which seems relevant to the topic. However, it does not address the use of microwave fields to dress the rotational states of molecules, which is a key aspect of the desired topic. The experiments are more concerned with the inherent universal behavior of losses and the influence of electric fields, not the microwave dressing as a method to control interactions.

 🔴 [31]
Linking Ultracold Polar Molecules A. V. Avdeenkov, ..., J. L. Bohn (2002)

We predict that pairs of polar molecules can be weakly bound together in an ultracold environment, provided that a dc electric field is present. The field that links the molecules together also strongly influences the basic properties of the resulting dimer, such as its binding energy and predissociation lifetime. Because of their long-range character these dimers will be useful in disentangling cold collision dynamics of polar molecules. As an example, we estimate the microwave photoassociation yield for OH-OH cold collisions.

Even though the paper delves into the association and behavior of ultracold polar molecules under the influence of a dc electric field, and touches upon the influence of microwaves in photoassociation spectroscopy, it does not seem to emphasize on microwave shielding of bialkali molecules specifically. The study primarily discusses the reactions and interactions of OH molecules and the influence of electric fields on their dimers' properties, with only a partial focus on microwaves' role. Furthermore, it seems to lack mention of the drastic impact of microwaves on the inelastic collision rates of bialkali molecules.

 🔴 [32]
A high quality, efficiently coupled microwave cavity for trapping cold molecules D. P. Dunseith, ..., M. R. Tarbutt (2014)

We characterize a Fabry-Perot microwave cavity designed for trapping atoms and molecules at the antinode of a microwave field. The cavity is fed from a waveguide through a small coupling hole. Focussing on the compact resonant modes of the cavity, we measure how the electric field profile, the cavity quality factor, and the coupling efficiency, depend on the radius of the coupling hole. We measure how the quality factor depends on the temperature of the mirrors in the range from 77 to 293K. The presence of the coupling hole slightly changes the profile of the mode, leading to increased diffraction losses around the edges of the mirrors and a small reduction in quality factor. We find the hole size that maximizes the intra-cavity electric field. We develop an analytical theory of the aperture-coupled cavity that agrees well with our measurements, with small deviations due to enhanced diffraction losses. We find excellent agreement between our measurements and finite-difference time-domain simulations of the cavity.

This paper discusses a microwave cavity designed for trapping cold molecules, including details of the electric field profile and the quality of the cavity. While it speaks to the trapping of ground-state molecules, and vaguely to their stability against collisions within microwave traps, it does not directly address the core subject of the researcher's interest - which is the shielding effect of microwave fields on bialkali molecules' inelastic collision rates in the presence of additional external fields. Moreover, the paper seems to focus more on the technical aspects of the microwave cavity's efficiency rather than on the molecular interaction potentials and their collision dynamics under external fields. Therefore, it might provide only a peripheral understanding of the environment in which bialkali molecules could be manipulated but doesn't specifically study the exact phenomenon of interest.

 🔴 [33]
Dipolar evaporation of reactive molecules to below the Fermi temperature Giacomo Valtolina, ..., Jun Ye (2020)

Molecules are the building blocks of matter and their control is key to the investigation of new quantum phases, where rich degrees of freedom can be used to encode information and strong interactions can be precisely tuned. Inelastic losses in molecular collisions, however, have greatly hampered the engineering of low-entropy molecular systems. So far, the only quantum degenerate gas of molecules has been created via association of two highly degenerate atomic gases. Here, we use an external electric field along with optical lattice confinement to create a two-dimensional (2D) Fermi gas of spin-polarized potassium-rubidium (KRb) polar molecules, where elastic, tunable dipolar interactions dominate over all inelastic processes. Direct thermalization among the molecules in the trap leads to efficient dipolar evaporative cooling, yielding a rapid increase in phase-space density. At the onset of quantum degeneracy, we observe the effects of Fermi statistics on the thermodynamics of the molecular gas. These results demonstrate a general strategy for achieving quantum degeneracy in dipolar molecular gases to explore strongly interacting many-body phases.

The paper in question describes an experimental setup for creating a 2D Fermi gas of KRb molecules using an external electric field and optical lattice confinement, and it focuses on using dipolar interactions to dominate over inelastic processes. While it does discuss controlling inelastic losses and thereby improving the lifetime of a molecular gas, it neither specifically addresses the use of a microwave field to dress rotational states, nor does it mention a change in collision rates due to the presence of a microwave shield. Instead, it appears to explore alternative methods such as dipolar evaporative cooling and Fermi statistics effects.

 🔴 [34]
Resonances in non-universal dipolar collisions Tijs Karman (2022)

Scattering resonances due to the dipole-dipole interaction between ultracold molecules, induced by static or microwave fields, are studied theoretically. We develop a method for coupled-channel calculations that can efficiently impose many short-range boundary conditions, defined by a short-range phase shift and loss probability as in quantum-defect theory. We study how resonances appear as the short-range loss probability is lowered below the universal unit probability. This may become realizable for nonreactive ultracold molecules in blue-detuned box potentials.

The presented paper 'Resonances in non-universal dipolar collisions' does explore the area of ultracold molecules squirming under the effect of external static or microwave electric fields. These fields induce dipole moments leading to dipole-dipole interactions between the molecules. The paper discusses tuning the long-range dipole-dipole interaction strength, creating potential impacts on bound states and scattering resonances. However, the paper seems to focus a great deal on scattering residues, which while related, is not the main focus of the desired topic. Furthermore, it does not appear to have a dedicated focus on bialkali molecules nor does it delve detailedly into the interaction potential between the bialkali molecules, which is of significant importance for the chosen topic.

 🔴 [35]
Long-range states and Feshbach resonances in collisions between ultracold alkali-metal diatomic molecules and atoms Matthew D. Frye, ..., Jeremy M. Hutson (2022)

We consider the long-range states expected for complexes formed from an alkali-metal diatomic molecule in a singlet state and an alkali-metal atom. We explore the structure of the Hamiltonian for such systems, and the couplings between the six angular momenta that are present. We consider the patterns and densities of the long-range states, and the terms in the Hamiltonian that can cause Feshbach resonances when the states cross threshold as a function of magnetic field. We present a case study of $^{40}$K$^{87}$Rb+$^{87}$Rb. We show multiple types of resonance due to long-range states with rotational and/or hyperfine excitation, and consider the likelihood of them existing at low to moderate magnetic fields.

The paper discusses the long-range states and Feshbach resonances in the ultracold collisions of diatomic alkali-metal molecules and atoms. Although it discusses some elements connected to the researcher's interest, such as the Feshbach resonances and ultracold collisions, it does not explicitly consider microwave shielding or the influence of such radiation in reducing inelastic collisions. However, references (26), (28) and (30) within the paper are directly related to microwave shielding of ultracold molecules, which would seem to be directly relevant to the topic of interest.

 🔴 [36]
Microwave trap for atoms and molecules S. C. Wright, ..., M. R. Tarbutt (2019)

We demonstrate a trap that confines polarizable particles around the antinode of a standing-wave microwave field. The trap relies only on the polarizability of the particles far from any resonances, so can trap a wide variety of atoms and molecules in a wide range of internal states, including the ground state. The trap has a volume of about 10 cm$^3$, and a depth approaching 1 K for many polar molecules. We measure the trap properties using $^{7}$Li atoms, showing that when the input microwave power is 610 W, the atoms remain trapped with a $1/e$ lifetime of 1.76(12) s, oscillating with an axial frequency of 28.55(5) Hz and a radial frequency of 8.81(8) Hz. The trap could be loaded with slow molecules from a range of available sources, and is particularly well suited to sympathetic cooling and evaporative cooling of molecules.

The provided paper 'Microwave trap for atoms and molecules' by S. C. Wright, T. E. Wall, and M. R. Tarbutt primarily discusses a type of microwave trap that capitalizes on the polarizability of particles to confine them, with no specific focus on bialkali molecules, microwave shielding, or external field influences on collision rates. While the concept of using microwave fields is somewhat related, the main topic of this paper seems to be the design and capabilities of a general microwave trap, rather than altering inelastic collision rates of bialkali molecules through rotation state manipulation in the presence of external fields. Given the researcher's precise interest in reducing inelastic collisions specifically for bialkali molecules, this paper does not sufficiently align with the goal of identifying literature that explores microwave shielding techniques or the impact of external fields on collision dynamics.

 🔴 [37]
Optical shielding of destructive chemical reactions between ultracold ground-state NaRb molecules T. Xie, ..., N. Bouloufa-Maafa (2020)

We propose a method to suppress the chemical reactions between ultracold bosonic ground-state $^{23}$Na$^{87}$Rb molecules based on optical shielding. By applying a laser with a frequency blue-detuned from the transition between the lowest rovibrational level of the electronic ground state $X^1\Sigma^+ (v_X=0, j_X=0)$, and the long-lived excited level $b^3\Pi_0 (v_b=0, j_b=1)$, the long-range dipole-dipole interaction between the colliding molecules can be engineered, leading to a dramatic suppression of reactive and photoinduced inelastic collisions, for both linear and circular laser polarizations. We demonstrate that the spontaneous emission from $b^3\Pi_0 (v_b=0, j_b=1)$ does not deteriorate the shielding process. This opens the possibility for a strong increase of the lifetime of cold molecule traps, and for an efficient evaporative cooling. We also anticipate that the proposed mechanism is valid for alkali-metal diatomics with sufficiently large dipole-dipole interactions.

While the paper primarily focuses on the optical shielding of ultracold molecules using a laser to suppress inelastic collisions, it does discuss the use of a microwave field tuned to the molecular rotation transition between two rotational sublevels. The paper explains how this can engineer repulsive long-range interactions between molecules and how can shape the rate of inelastic collisions. However, the paper seems to consider microwave shielding as a secondary aspect and is more focused on optical shielding instead. Moreover, the role of external electric or magnetic fields, fundamental to the specific topic the researcher is interested in, doesn’t seem to be extensively discussed. An interesting mention in the paper though, is about the fact that circularly-polarized microwave field might be more successful for shielding, though challenging to implement. However, the context and details of this aspect are not excerpted from the main content and it’s unclear how in-depth the paper goes into this.

 🔴 [38]
Efficient Pathway to NaCs Ground State Molecules Claire Warner, ..., Sebastian Will (2023)

We present a study of two-photon pathways for the transfer of NaCs molecules to their rovibrational ground state. Starting from NaCs Feshbach molecules, we perform bound-bound excited state spectroscopy in the wavelength range from 900~nm to 940~nm, covering more than 30 vibrational states of the $c \, ^3\Sigma^+$, $b \, ^3\Pi$, and $B \, ^1\Pi$ electronic states. Analyzing the rotational substructure, we identify the highly mixed $c \, ^3\Sigma^+_1 \, |v=22 \rangle \sim b \, ^3\Pi_1 \, | v=54\rangle$ state as an efficient bridge for stimulated Raman adiabatic passage (STIRAP). We demonstrate transfer into the NaCs ground state with an efficiency of up to 88(4)\%. Highly efficient transfer is critical for the realization of many-body quantum phases of strongly dipolar NaCs molecules and high fidelity detection of single molecules, for example, in spin physics experiments in optical lattices and quantum information experiments in optical tweezer arrays.

This paper is primarily about the study of two-photon pathways for the transfer of NaCs molecules to their rovibrational ground state. However, it does not directly focus on the impact of external microwave fields on bialkali molecules like NaCs and their inelastic collision rates. The main objective of this work revolves around presenting a pathway for NaCs molecules to achieve their rovibrational ground state more efficiently through Stimulated Raman Adiabatic Passage (STIRAP). Hence, while it indirectly provides valuable insights about bialkali molecules and their interaction potentials, it does not address the specific topic of microwave shielding and its implications for inelastic collision rates.

 🔴 [39]
A High Phase-Space Density Gas of NaCs Feshbach Molecules Aden Z. Lam, ..., Sebastian Will (2022)

We report on the creation of ultracold gases of bosonic Feshbach molecules of NaCs. The molecules are associated from overlapping gases of Na and Cs using a Feshbach resonance at 864.12(5) G. We characterize the Feshbach resonance using bound state spectroscopy, in conjunction with a coupled-channel calculation. By varying the temperature and atom numbers of the initial atomic mixtures, we demonstrate the association of NaCs gases over a wide dynamic range of molecule numbers and temperatures, reaching 70 nK for our coldest systems and a phase-space density near 0.1. This is an important stepping-stone for the creation of degenerate gases of strongly dipolar NaCs molecules in their absolute ground state.

This paper reports the creation of ultracold NaCs Feshbach molecules and does discuss the association of these molecules using a Feshbach resonance, which is a technique relevant for manipulating molecular states and inelastic collision properties. However, it focuses more on the creation and characterization of a high phase-space density gas of NaCs molecules rather than directly discussing microwave shielding and its impact on inelastic collision rates in the presence of external electric or magnetic fields. The selected references within the paper do mention other papers which are directly focused on 'microwave shielding' (e.g., refs. 56 and 57) and 'controlling scattering of dipolar molecules' (e.g., refs. 58 and 60), which suggests that while this paper is in the vicinity of the subject, it may not specifically address the topic of how microwave shielding modifies inelastic collision rates under external electric or magnetic field influence.

 🔴 [40]
Ultracold Gas of Dipolar NaCs Ground State Molecules Ian Stevenson, ..., Sebastian Will (2022)

We report on the creation of bosonic NaCs molecules in their absolute rovibrational ground state via stimulated Raman adiabatic passage. We create ultracold gases with up to 22,000 dipolar NaCs molecules at a temperature of 300(50) nK and a peak density of $1.0(4) \times 10^{12}$ cm$^{-3}$. We demonstrate comprehensive quantum state control by preparing the molecules in a specific electronic, vibrational, rotational, and hyperfine state. Employing the tunability and strength of the permanent electric dipole moment of NaCs, we induce dipole moments of up to 2.6 D. Dipolar systems of NaCs molecules are uniquely suited to explore strongly interacting phases in dipolar quantum matter.

The paper discusses the use of stimulated Raman adiabatic passage to create an ultracold gas of NaCs ground state molecules, a bialkali molecule. It discusses controlling the state of the molecules, suggesting sophisticated understanding of the relevant physics, which is relevant background to the main topic of interest. Further, the concept of dipolar molecules in quantum systems, and the strong influence of the dipole moment, is relevant, as it may impact collision dynamics. Finally, the paper does mention the use of microwave shielding to suppress lossy two-body collisions; however, it is not the main focus of the paper and does not discuss the use of external electric or magnetic fields in this process. Hence, the paper is closely tied with the researcher's topic, but misses out on some key specifics.

 🔴 [41]
Electric field suppression of ultracold confined chemical rates Goulven Quéméner, ..., John L. Bohn (2010)

We consider ultracold collisions of polar molecules confined in a one dimensional optical lattice. Using a quantum scattering formalism and a frame transformation method, we calculate elastic and chemical quenching rate constants for fermionic molecules. Taking KRb molecules as a prototype, we find that the rate of quenching collisions is enhanced at zero electric field as the confinement is increased, but that this rate is suppressed when the electric field is turned on. For molecules with 500 nK of collision energy, for realistic molecular densities, and for achievable experimental electric fields and trap confinements, we predict lifetimes of KRb molecules of 1 s. We find a ratio of elastic to quenching collision rates of about 100, which may be sufficient to achieve efficient experimental evaporative cooling of polar KRb molecules.

The paper focuses on the ultracold collisions of polar molecules, specifically KRb, within a one-dimensional optical lattice, discussing the effect of electric fields on the rate of chemical quenching. It seems to specifically address the influence of electric fields on collision rates but does not mention external microwave shielding or the presence of magnetic fields. Additionally, it seems to be oriented towards an electric field as a suppressant, not necessarily a microwave field as a dress state modifier for the molecules. Therefore, while it studies a related aspect (electric field effects on polar molecules), it does not directly examine the role of microwave shielding on inelastic collision rates in the presence of external fields.

 🔴 [42]
Quantum gas microscopy of Rydberg macrodimers Simon Hollerith, ..., Christian Gross (2018)

A microscopic understanding of molecules is essential for many fields of natural sciences but their tiny size hinders direct optical access to their constituents. Rydberg macrodimers - bound states of two highly-excited Rydberg atoms - feature bond lengths easily exceeding optical wavelengths. Here we report on the direct microscopic observation and detailed characterization of such macrodimers in a gas of ultracold atoms in an optical lattice. The size of about 0.7 micrometers, comparable to the size of small bacteria, matches the diagonal distance of the lattice. By exciting pairs in the initial two-dimensional atom array, we resolve more than 50 vibrational resonances. Using our spatially resolved detection, we observe the macrodimers by correlated atom loss and demonstrate control of the molecular alignment by the choice of the vibrational state. Our results allow for precision testing of Rydberg interaction potentials and establish quantum gas microscopy as a powerful new tool for quantum chemistry.

While this paper contributes valuable insights into the field of quantum gas microscopy and quantum chemistry, including observations of Rydberg macrodimers and related interaction potentials, it does not specifically delve into the effect of microwave shielding on inelastic collisions in bialkali molecules. The controlled association of these molecules and the utilization of an external electric/magnetic field to affect inelastic collision rates—central aspects of the desired topic—are not mentioned. Rather, this paper focuses more on molecular structure analysis using quantum gas microscopy and Rydberg macrodimers, which doesn't align directly with the specific topic of interest.

 🔴 [43]
A Feshbach resonance in collisions between ultracold ground state molecules Juliana J. Park, ..., Wolfgang Ketterle (2022)

Collisional resonances are an important tool which has been used to modify interactions in ultracold gases, for realizing novel Hamiltonians in quantum simulations, for creating molecules from atomic gases and for controlling chemical reactions. So far, such resonances have been observed for atom-atom collisions, atom-molecule collisions and collisions between Feshbach molecules which are very weakly bound. Whether such resonances exist for ultracold ground state molecules has been debated due to the possibly high density of states and/or rapid decay of the resonant complex. Here we report a very pronounced and narrow (25 mG) Feshbach resonance in collisions between two ground state NaLi molecules. This molecular Feshbach resonance has two special characteristics. First, the collisional loss rate is enhanced by more than two orders of magnitude above the background loss rate which is saturated at the $p$-wave universal value, due to strong chemical reactivity. Second, the resonance is located at a magnetic field where two open channels become nearly degenerate. This implies the intermediate complex predominantly decays to the second open channel. We describe the resonant loss feature using a model with coupled modes which is analogous to a Fabry-P\'erot cavity. Our observations prove the existence of long-lived coherent intermediate complexes even in systems without reaction barriers and open up the possibility of coherent control of chemical reactions.

The paper focuses on the utilization of Feshbach resonances in collisions between ultracold ground-state NaLi molecules, and how this impacts the loss rate, which is analogous to inelastic collisions. Importantly, the paper discusses the use of external electric or magnetic fields in tuning intermolecular interactions, which is very much relevant to the desired topic. However, the paper doesn't explicitly discuss the role of microwave fields in manipulating the rotational states of these molecules, which is a crucial aspect of the research topic at hand. While the paper might provide insightful information, particularly with respect to resonance-caused inelastic collisions and the role of external fields, it seems to miss the specific intervention of microwave fields and their impact on the inelastic collision rate of the bialkali molecules specifically KRb, RbCs, NaK, and NaCs.

 🔴 [44]
Statistical Aspects of Ultracold Resonant Scattering Michael Mayle, ..., John L. Bohn (2012)

Compared to purely atomic collisions, ultracold collisions involving molecules have the potential to support a much larger number of Fano-Feshbach resonances due to the huge amount of ro-vibrational states available. In order to handle such ultracold atom-molecule collisions, we formulate a theory that incorporates the ro-vibrational Fano-Feshbach resonances in a statistical manner while treating the physics of the long-range scattering, which is sensitive to such things as hyperfine states, collision energy and any applied electromagnetic fields, exactly within multichannel quantum defect theory. Uniting these two techniques, we can assess the influence of highly resonant scattering in the threshold regime, and in particular its dependence on the hyperfine state selected for the collision. This allows us to explore the onset of Ericson fluctuations in the regime of overlapping resonances, which are well-known in nuclear physics but completely unexplored in the ultracold domain.

This article investigates ultracold atom-molecule collisions using multichannel quantum defect theory and statistical models. The theory focuses on collision dynamics under external electromagnetic fields. However, the paper seems to center on Fano-Feshbach resonances and ultracold scattering, with the selected components discussing atom-diatom collisions. While it seems relevant to ultracold collisions and how external electromagnetic fields influence them, it doesn't directly address the interaction of bialkali molecules with microwave fields, nor does it clearly focus on inelastic collisions. There's no mention of 'microwave shielding,' and the subject of bialkali molecules isn't clear.

 🔴 [45]
Cold polar molecules in 2D traps: Tailoring interactions with external fields for novel quantum phases A. Micheli, ..., P. Zoller (2007)

We discuss techniques to engineer effective long-range interactions between polar molecules using external static electric and microwave fields. We consider a setup where molecules are trapped in a two-dimensional pancake geometry by a far-off-resonance optical trap, which ensures the stability of the dipolar collisions. We detail how to modify the shape and the strength of the long-range part of interaction potentials, which can be utilized to realize interesting quantum phases in the context of cold molecular gases.

This paper touches upon the application of external electric and microwave fields to alter the interactions between cold polar molecules trapped in a two-dimensional geometry. Although this research does not directly focus on bialkali molecules, the techniques discussed could provide useful insights into their microwave shielding given their similar polar characteristics. However, the paper seems to focus more on modifying the long-range part of interaction potentials to realize interesting quantum phases, rather than influencing the inelastic collision rates.

 🔴 [46]
Cold and Ultracold Molecules: Science, Technology, and Applications Lincoln D. Carr, ..., Jun Ye (2009)

This article presents a review of the current state of the art in the research field of cold and ultracold molecules. It serves as an introduction to the Special Issue of the New Journal of Physics on Cold and Ultracold Molecules and describes new prospects for fundamental research and technological development. Cold and ultracold molecules may revolutionize physical chemistry and few body physics, provide techniques for probing new states of quantum matter, allow for precision measurements of both fundamental and applied interest, and enable quantum simulations of condensed-matter phenomena. Ultracold molecules offer promising applications such as new platforms for quantum computing, precise control of molecular dynamics, nanolithography, and Bose-enhanced chemistry. The discussion is based on recent experimental and theoretical work and concludes with a summary of anticipated future directions and open questions in this rapidly expanding research field.

This paper undoubtedly discusses ultracold molecules, their potential for quantum computing, precise control of molecular dynamics, and related applications. It even hints at the use of electric and/or magnetic fields to adjust molecular energy levels to suppress inelastic processes and considers inelastic collisions between microwave-dressed molecules in a supposed microwave-frequency trap. But, the focus is broader and not specific to bialkali molecules or the exact modulation of the inelastic collision rate. Furthermore, the paper seems to be a review, not presenting original research about the topic in question, though it could still provide useful references.

 🔴 [47]
Formation and interactions of cold and ultracold molecules: new challenges for interdisciplinary physics Olivier Dulieu, ..., Carlo Gabbanini (2009)

Progress on researches in the field of molecules at cold and ultracold temperatures is reported in this review. It covers extensively the experimental methods to produce, detect and characterize cold and ultracold molecules including association of ultracold atoms, deceleration by external fields and kinematic cooling. Confinement of molecules in different kinds of traps is also discussed. The basic theoretical issues related to the knowledge of the molecular structure, the atom-molecule and molecule-molecule mutual interactions, and to their possible manipulation and control with external fields, are reviewed. A short discussion on the broad area of applications completes the review.

The provided paper offers valuable insights into experimental methods for producing, detecting, and characterizing cold and ultracold molecules, including bialkali systems. However, while it covers the manipulation of molecules with external fields and discusses molecule-molecule interactions, there is no specific mention of using microwave fields to shield these molecules or modify the collision rates. The excerpt provided talks about Feshbach resonances and molecule formation, which are related to molecular interactions in a broader sense but do not fulfill the specific criteria of the desired topic regarding microwave shielding and collision rate alteration. Furthermore, the paper seems to be a broader review of the field rather than focused on the niche topic of microwave shielding.

 🔴 [48]
Seconds-scale coherence on nuclear spin transitions of ultracold polar molecules in 3D optical lattices Junyu Lin, ..., Dajun Wang (2021)

Ultracold polar molecules (UPMs) are emerging as a novel and powerful platform for fundamental applications in quantum science. Here, we report characterization of the coherence between nuclear spin levels of ultracold ground-state sodium-rubidium molecules loaded into a 3D optical lattice with a nearly photon scattering limited trapping lifetime of 9(1) seconds. After identifying and compensating the main sources of decoherence, we achieve a maximum nuclear spin coherence time of $T_2^* = 3.3(6)$~s with two-photon Ramsey spectroscopy. Furthermore, based on the understanding of the main factor limiting the coherence of the two-photon Rabi transition, we obtain a Rabi lineshape with linewidth below 0.8 Hz. The simultaneous realization of long lifetime and coherence time, and ultra-high spectroscopic resolution in our system unveils the great potentials of UPMs in quantum simulation, computation, and metrology.

The provided paper primarily focuses on coherence between nuclear spin levels of ultracold sodium-rubidium molecules in optical lattices and does not directly address the use of microwave shielding to adjust inelastic collision rates in the presence of external fields. While references [19], [20], and [21] hint at studies related to the control of molecular interactions and collision rates, they seem more aligned with electric field use and dipolar interactions than specifically microwave shielding. Therefore, the core content of the paper appears to diverge from the specific interest in microwave shielding effects on inelastic collision rates in bialkali molecules.

 🔴 [49]
Long-lived fermionic Feshbach molecules with tunable $p$-wave interactions Marcel Duda, ..., Xin-Yu Luo (2022)

Ultracold fermionic Feshbach molecules are promising candidates for exploring quantum matter with strong $p$-wave interactions, however, their lifetimes were measured to be short. Here, we characterize the $p$-wave collisions of ultracold fermionic $^{23}\mathrm{Na}^{40}\mathrm{K}$ Feshbach molecules for different scattering lengths and temperatures. By increasing the binding energy of the molecules, the two-body loss coefficient reduces by three orders of magnitude leading to a second-long lifetime, 20 times longer than that of ground-state molecules. We exploit the scaling of elastic and inelastic collisions with the scattering length and temperature to identify a regime where the elastic collisions dominate over the inelastic ones allowing the molecular sample to thermalize. Our work provides a benchmark for four-body calculations of molecular collisions and is essential for producing a degenerate Fermi gas of Feshbach molecules.

The examined paper primarily discusses the longevity and $p$-wave interaction characteristics of ultracold fermionic $^{23}\mathrm{Na}^{40}\mathrm{K}$ Feshbach molecules, a specific type of bialkali molecule. It focuses on empirical findings related to the differing strengths of elastic and inelastic collisions at various scattering lengths and temperatures, and how the binding energy of these molecules affects collisional loss. Whether these results translate to scenarios where microwave shielding is used in presence of external fields is not explicitly mentioned. Moreover, there is no direct reference to microwave field induced effects on the inelastic collision rates or the modification of the interaction potential via rotational state dressing. While the paper contributes to the broader field of ultracold bialkali molecular studies, it does not appear to specifically address microwave shielding in the context of modifying inelastic collision rates.

 🔴 [50]
Prospects for making polar molecules with microwave fields Svetlana Kotochigova (2007)

We propose a new mechanism to produce ultracold polar molecules with microwave fields. The proposed mechanism converts trapped ultracold atoms of different species into vibrationally excited molecules by a single microwave transition and entirely depends on the existence of a permanent dipole moment in the molecules. As opposed to production of molecules by photoassociation or magnetic-field Feshbach resonances our method does not rely on the structure and lifetime of excited states or existence of Feshbach resonances. In addition, we determine conditions for optimal creation of polar molecules in vibrationally excited states of the ground-state potential by changing frequency and intensity of the microwave field. We also explore the possibility to produce vibrationally cold molecules by combining the microwave field with an optical Raman transition or by applying a microwave field to Feshbach molecules. The production mechanism is illustrated for two polar molecules: KRb and RbCs.

The paper discusses a new mechanism to create ultracold polar molecules, including the bialkali molecules KRb and RbCs, using microwave fields. However, the primary aim is to convert atoms into molecules and optimally create vibrationally excited states, which is different from shielding molecules to prevent inelastic collisions. While it does involve the use of microwave fields and touches on related molecules, the main goal of the research does not align with the specified topic of shielding these molecules to drastically change the inelastic collision rate. Therefore, it lacks a specific focus on altering the collision rates of already formed molecules via microwave shielding, which is the key interest of the desired topic.

 🔴 [51]
Tuning ultracold collisions of excited rotational dipolar molecules Gaoren Wang, ..., Goulven Quéméner (2014)

We investigate the ultracold collisions of rotationally excited dipolar molecules in free-space, taking the hetero-nuclear bi-alkali molecule of KRb as an example. We show that we can sharply tune the elastic, inelastic and reactive rate coefficients of lossy molecular collisions when a second rotationally excited colliding channel crosses the threshold of the initial colliding channel, with the help of an applied electric field, as found by Avdeenkov et al. for non-lossy molecules [Phys. Rev. A 73, 022707 (2006)]. We can increase or decrease the loss processes whether the second channel is above or below the initial channel. This is seen for both bosonic and fermionic molecules. Additionally, we include the electric quadrupole and octopole moment to the dipole moment in the expression of the long-range multipole-multipole interaction. We found that for processes mediated by the incident channel like elastic and loss collisions, the inclusion of quadrupole and octopole moments are not important at ultralow energies. They are important for processes mediated by state-to-state transitions like inelastic collisions.

While the paper investigates the effect of electric fields and rotationally excited states on inelastic collision rates of dipolar molecules (using the bialkali molecule of KRb as an example) it does not specifically address microwave shielding as a method of altering collision rates. Instead, it attempts to use the anisotropy of the dipole-dipole interaction and external electric fields to adjust collision rates. Although some principles might be applicable to the topic of interest, it cannot serve as a principal paper for the exact investigation sought.

 🔴 [52]
Adimensional theory of shielding in ultracold collisions of dipolar rotors Maykel L. González-Martínez, ..., Goulven Quéméner (2017)

We investigate the electric field shielding of ultracold collisions of dipolar rotors, initially in their first rotational excited state, using an adimensional approach. We establish a map of good and bad candidates for efficient evaporative cooling based on this shielding mechanism, by presenting the ratio of elastic over quenching processes as a function of a rescaled rotational constant $\tilde{B} = B/s_{E_3}$ and a rescaled electric field $\tilde{F} = dF/B$. $B, d, F, s_{E_3}$ are respectively the rotational constant, the full electric dipole moment of the molecules, the applied electric field and a characteristic dipole-dipole energy. We identify two groups of bi-alkali dipolar molecules. The first group, including RbCs, NaK, KCs, LiK, NaRb, LiRb, NaCs and LiCs, is favorable with a ratio over 1000 at collision energies equal (or even higher) to their characteristic dipolar energy. The second group, including LiNa and KRb, is not favorable. More generally, for molecules well described by Hund's case b, our adimensional study provides the conditions of efficient evaporative cooling. The range of appropriate rescaled rotational constant and rescaled field is approximately $\tilde{B} \ge 10^8$ and $3.25 \le \tilde{F} \le 3.8$, with a maximum ratio reached for $\tilde{F} \simeq 3.4$ for a given $\tilde{B}$. We also discuss the importance of the electronic van der Waals interaction on the adimensional character of our study.

The paper discusses the shielding of ultracold collisions among dipolar rotors, specifically focusing on bialkali molecules in an external electric field. Though the article provides a theoretical framework for understanding the shielding mechanism in dipolar bialkali molecules and discusses the conditions for efficient evaporative cooling, it does not specifically address microwave shielding or the modulation of inelastic collision rates by manipulating rotational states using microwaves. Furthermore, there is no mention of the presence of magnetic fields which is a part of the desired topic area.

 🔴 [53]
Prospects for sympathetic cooling of molecules in electrostatic, ac and microwave traps S. K. Tokunaga, ..., M. R. Tarbutt (2010)

We consider how trapped molecules can be sympathetically cooled by ultracold atoms. As a prototypical system, we study LiH molecules co-trapped with ultracold Li atoms. We calculate the elastic and inelastic collision cross sections of LiH + Li with the molecules initially in the ground state and in the first rotationally excited state. We then use these cross sections to simulate sympathetic cooling in a static electric trap, an ac electric trap, and a microwave trap. In the static trap we find that inelastic losses are too great for cooling to be feasible for this system. The ac and microwave traps confine ground-state molecules, and so inelastic losses are suppressed. However, collisions in the ac trap can take molecules from stable trajectories to unstable ones and so sympathetic cooling is accompanied by trap loss. In the microwave trap there are no such losses and sympathetic cooling should be possible.

The paper under consideration explores the use of a microwave trap to confine ground-state molecules, like LiH, and its implications on inelastic collision rates and sympathetic cooling in different types of traps, including electric and microwave traps. While it mentions the suppression of inelastic losses in microwave traps, it does not specifically discuss the shielding effect on various bialkali molecules (KRb, RbCs, NaK, NaCs) as stated in the desired topic. The focus is on LiH molecules and the general concept of a microwave trap rather than the specific interaction potential modification of bialkali molecules. Additionally, no explicit mention of altering the inelastic collision rate by external electric or magnetic fields is made as related to bialkali molecules.

 🔴 [54]
Model for two-body collisions between ultracold dipolar molecules around a Förster resonance in an electric field Lucas Lassablière, ..., Goulven Quéméner (2022)

We propose a one-channel, simple model to describe the dynamics of ultracold dipolar molecules around a F\"orster resonance. Slightly above a specific electric field, a collisional shielding can take place, suppressing the molecular losses in a gas. The overall description of the quantum physical mechanism comes back to the dynamics on a unique energy surface, which depends on the relative distance and angular approach of the molecules. This surface enables to interpret how the dipole moments of the molecules are induced and interlocked by the electric field and the dipole-dipole interaction during the process, especially when the shielding is triggered. Averaging the relative angular motion over a unique partial wave (the lowest one when the ultracold regime is reached), the model reproduces well the behaviour of the rate coefficients observed experimentally and predicted theoretically [Matsuda et al., Science 370, 1324 (2020); Li et al., Nat. Phys. 17, 1144 (2021)]. This economic model encapsulates the main physics of the quantum process. Therefore, it can be used as an alternative to a full quantum dynamical treatment and is promising for future studies of collisions involving more bodies.

The presented paper discusses dipolar molecules in an electric field context, where considerable emphasis is on collisional shielding and its impact on molecular loss. Most notably, it describes how an electric field can trigger a shielding mechanism, minimizing inelastic collisions, which aligns with your topic's component of minimizing such collisions via field manipulation. However, the paper rather focuses on electric field shielding, not microwave shielding. Moreover, though it appears to discuss fermionic 40K87Rb molecules (a type of bialkali molecule), it does not affirmatively talk about how external electric or magnetic fields would alter the inelastic collision rates in the context of microwave shielding. Thus the paper seems to address parts of your topic but misses the specific context of microwave shielding.

 🔴 [55]
Stable Topological Superfluid Phase of Ultracold Polar Fermionic Molecules N. R. Cooper, ..., G. V. Shlyapnikov (2009)

We show that single-component fermionic polar molecules confined to a 2D geometry and dressed by a microwave field, may acquire an attractive $1/r^3$ dipole-dipole interaction leading to superfluid p-wave pairing at sufficiently low temperatures even in the BCS regime. The emerging state is the topological $p_x+ip_y$ phase promising for topologically protected quantum information processing. The main decay channel is via collisional transitions to dressed states with lower energies and is rather slow, setting a lifetime of the order of seconds at 2D densities $\sim 10^8$ cm$^{-2}$.

While the paper does discuss the effect of microwave fields on polar fermionic molecules (which include bialkali molecules) leading to a change in inelastic collision rates, it seems to focus primarily on the superfluid phase of these molecules and their applications in quantum information processing. The paper also addresses the reduced inelastic collision rates due to microwave dressing in a 2D confined system but lacks specific mention of the presence of additional electric or magnetic fields. The results reflect a general trend toward reduced inelastic losses and discuss the manipulation of inelastic scattering rates. However, the main context seems somewhat tangential to the described goal of the researcher because it is more concerned with the resultant superfluid states rather than explicitly focusing on the mechanism of microwave shielding in the presence of electric or magnetic fields to change collision rates.

 🔴 [56]
Singlet Pathway to the Ground State of Ultracold Polar Molecules Anbang Yang, ..., Kai Dieckmann (2019)

Starting from weakly bound Feshbach molecules, we demonstrate a two-photon pathway to the dipolar ground state of bi-alkali molecules that involves only singlet-to-singlet optical transitions. This pathway eliminates the search for a suitable intermediate state with sufficient singlet-triplet mixing and the exploration of its hyperfine structure, as is typical for pathways starting from triplet dominated Feshbach molecules. By selecting a Feshbach state with a stretched singlet hyperfine component and controlling the polarization of the excitation laser, we assure coupling to only a single hyperfine component of the $\textrm{A}^{1}\Sigma^{+}$ excited potential, even if the hyperfine structure is not resolved. Similarly, we address a stretched hyperfine component of the $\textrm{X}^{1}\Sigma^{+}$ rovibrational ground state, and therefore an ideal three level system is established. We demonstrate this pathway with ${}^{6}\textrm{Li}{}^{40}\textrm{K}$ molecules. By exploring deeply bound states of the $\textrm{A}^{1}\Sigma^{+}$ potential, we are able to obtain large and balanced Rabi frequencies for both transitions. This method can be applied to other molecular species.

The paper under review deals primarily with the production of ultracold polar molecules exploiting Feshbach resonances and STIRAP, focusing on the creation of ultracold dipolar quantum gases, their structural analysis, and potential applications. It does not specifically dive into the use of a microwave field to shield bialkali molecules or the influence of external electric/magnetic fields assisting to modulate the inelastic collision rate. There's no explicit discussion referring to the core topic of interest which is altering the interaction potential of bialkali molecules using microwave fields, impacting collision dynamics.

 🔴 [57]
Observation of resonant dipolar collisions in ultracold $^{23}$Na$^{87}$Rb rotational mixtures Junyu He, ..., Dajun Wang (2020)

We report the investigation on dipolar collisions in rotational state mixtures of ultracold bosonic $^{23}$Na$^{87}$Rb molecules. The large resonant dipole-dipole interaction between molecules in rotational states of opposite parities brings about significant modifications to their collisions, even when an electric field is not present. In this work, this effect is revealed by measuring the dramatically enhanced two-body loss rate constants in the mixtures. In addition, the dipolar interaction strength can be tuned by preparing the NaRb mixture in different rotational levels with microwave spectroscopy. When the rotational level combination is not of the lowest energy, contributions from hyperfine changing collisions are also observed. Our measured loss rate constants are in good agreement with a quantum close-coupling calculation which we also present in full detail.

The paper discusses the observation of resonant dipolar collisions in ultracold bialkali molecules - specifically, Sodium Rubidium (NaRb), a key type of molecule in question here. It does tackle the interaction potential changes due to rotational state changes, a fundamental aspect of microwave shielding. The paper also talks about the enhanced two-body loss rate constants which can be associated with inelastic collisions, being amendable by microwave spectroscopy. However, despite touching upon the role of external fields, it does not discuss the specifics of 'microwave shielding' or discuss the direct role of external electric or magnetic fields on altering the inelastic collision rate, only a lack of an electric field.

 🔴 [58]
Stimulated Raman adiabatic passage in physics, chemistry and beyond Nikolay V. Vitanov, ..., Klaas Bergmann (2016)

The technique of stimulated Raman adiabatic passage (STIRAP), which allows efficient and selective population transfer between quantum states without suffering loss due to spontaneous emission, was introduced in 1990 (Gaubatz \emph{et al.}, J. Chem. Phys. \textbf{92}, 5363, 1990). Since then STIRAP has emerged as an enabling methodology with widespread successful applications in many fields of physics, chemistry and beyond. This article reviews the many applications of STIRAP emphasizing the developments since 2000, the time when the last major review on the topic was written (Vitanov \emph{et al.}, Adv. At. Mol. Opt. Phys. \textbf{46}, 55, 2001). A brief introduction into the theory of STIRAP and the early applications for population transfer within three-level systems is followed by the discussion of several extensions to multi-level systems, including multistate chains and tripod systems. The main emphasis is on the wide range of applications in atomic and molecular physics (including atom optics, cavity quantum electrodynamics, formation of ultracold molecules, precision experiments, etc.), quantum information (including single- and two-qubit gates, entangled-state preparation, etc.), solid-state physics (including processes in doped crystals, nitrogen-vacancy centers, superconducting circuits, etc.), and even some applications in classical physics (including waveguide optics, frequency conversion, polarization optics, etc.). Promising new prospects for STIRAP are also presented (including processes in optomechanics, detection of parity violation in molecules, spectroscopy of core-nonpenetrating Rydberg states, and population transfer with X-ray pulses).

While the paper does offer an extensive overview of the STIRAP technique and its applications, including in the formation of ultracold molecules and quantum information, it does not specifically address the study of inelastic collision rates of bialkali molecules in the presence of electric or magnetic fields. Although STIRAP is a technique that could theoretically be part of the control methods used to manage inelastic collisions, the paper, based on the provided abstract and selected parts, does not focus on the interaction between microwave fields and external electric or magnetic fields in the context of modifying inelastic collisions in bialkali molecules. Therefore, the paper appears to be more general and encompassing than the narrowly defined topic of interest.

 🔴 [59]
Electro-association of ultracold dipolar molecules into tetramer field-linked states Goulven Quéméner, ..., James F. E. Croft (2023)

The presence of electric or microwave fields can modify the long-range forces between ultracold dipolar molecules in such a way as to engineer weakly-bound states of molecule pairs. These so-called field-linked states [Avdeenkov et al., Phys. Rev. Lett. 90, 043006 (2003), Lassabli\`ere et al., Phys. Rev. Lett. 121, 163402 (2018)], in which the separation between the two bound molecules can be orders of magnitude larger than the molecules themselves, have been observed as resonances in scattering experiments [Chen et al., Nature 614, 59 (2023)]. Here, we propose to use them as tools for the assembly of weakly-bound tetramer molecules, by means of ramping an electric field, the electric-field analog of magneto-association in atoms. This ability would present new possibilities for constructing ultracold polyatomic molecules.

The paper discusses engineering of field-linked states (FLS) by applying external fields, which strongly suggests relevance to the modification of interaction potentials between ultracold molecules, such as those mentioned in the topic. While the paper focuses more on the formation of weakly-bound tetramer molecules and the control of scattering length, it does cite the ability to tune this length and potentially shield the molecules against losses, which implies a relation to inelastic collision rates. However, the explicit focus on 'microwave shielding' of bialkali molecules in the context of inelastic collision rates is not the central theme of the paper. Instead, the paper addresses the broader context of molecule interaction control, which encompasses the desired topic but may not specifically focus on the inelastic collision rate modifications due to microwave fields and external fields.

 🔴 [60]
Photo-induced two-body loss of ultracold molecules Arthur Christianen, ..., Tijs Karman (2019)

The lifetime of nonreactive ultracold bialkali gases was conjectured to be limited by sticky collisions amplifying three-body loss. We show that the sticking times were previously overestimated and do not support this hypothesis. We find that electronic excitation of NaK+NaK collision complexes by the trapping laser leads to the experimentally observed two-body loss. We calculate the excitation rate with a quasiclassical, statistical model employing ab initio potentials and transition dipole moments. Using longer laser wavelengths or repulsive box potentials may suppress the losses.

The paper in question deals with the investigation of two-body loss in ultracold bialkali gases, specifically focusing on electronic excitation by trapping lasers as a cause for this loss. Although this topic is related to the overall study of inelastic collisions and lifetime of bialkali molecules, it does not directly address the use of microwave shielding or the application of external electric or magnetic fields to change inelastic collision rates. Instead, it suggests that using longer laser wavelengths or repulsive box potentials may suppress these losses, which is a different approach from what is requested.

 🔴 [61]
Microwave spectroscopy of radio-frequency dressed $^{87}$Rb G. A. Sinuco-Leon, ..., T. Fernholz (2019)

We study the hyperfine spectrum of atoms of $^{87}$Rb dressed by a radio-frequency field, and present experimental results in three different situations: freely falling atoms, atoms trapped in an optical dipole trap and atoms in an adiabatic radio-frequency dressed shell trap. In all cases, we observe several resonant side bands spaced (in frequency) at intervals equal to the dressing frequency, corresponding to transitions enabled by the dressing field. We theoretically explain the main features of the microwave spectrum, using a semi-classical model in the low field limit and the Rotating Wave Approximation for alkali-like species in general and $^{87}$Rb atoms in particular. As a proof of concept, we demonstrate how the spectral signal of a dressed atomic ensemble enables an accurate determination of the dressing configuration and the probing microwave field.

The paper focuses on radio-frequency (RF) dressing of $^{87}$Rb atoms and their response to microwave (MW) fields, which involves similar concepts to microwave shielding. However, the paper investigates the hyperfine spectra of atoms instead of inelastic collisions between bialkali molecules. Moreover, the study is specific to $^{87}$Rb atoms and does not explore interactions between molecules, bialkali or otherwise. While the manipulation of internal states via MW and RF fields is related to the desired topic, the focus on atomic interactions and hyperfine structures suggests the paper does not address the crucial aspects of inelastic collision rates in bialkali molecules, nor does it deal with the alteration of interaction potentials between molecules.

 🔴 [62]
Quantum state resolved molecular dipolar collisions over four decades of energy Guoqiang Tang, ..., Sebastiaan Y. T. van de Meerakker (2023)

Collisions between cold polar molecules represent a fascinating research frontier, but have proven hard to probe experimentally. We report measurements of inelastic cross sections for collisions between NO and ND 3 molecules at energies between 0.1 and 580 cm-1 , with full quantum state resolution. At energies below the 100 cm-1 well depth of the interaction potential, we observed backward glories originating from peculiar U-turn trajectories. At energies below 0.2 cm-1, we observed a breakdown of the Langevin capture model, which we interpreted in terms of a suppressed mutual polarization during the collision, effectively switching off the molecular dipole moments. Scattering calculations based on an ab initio NO-ND3 potential energy surface revealed the crucial role of near-degenerate rotational levels with opposite parity in low-energy dipolar collisions.

The paper describes experiments on molecular collisions involving polar molecules, specifically NO and ND3, and discussions on the effects of external fields on molecular interactions. However, it does not explicitly mention the use of microwaves for controlling collision rates or dressing rotational states of bialkali molecules. Additionally, NO and ND3 are not bialkali molecules. While the paper does delve into cold molecular collisions and the role of external fields, the absence of discussion on 'microwave shielding' or 'bialkali molecules' makes it less relevant to the specific topic of interest.

 🔴 [63]
Inelastic collisions of ultracold triplet Rb$_\textbf{2}$ molecules in the rovibrational ground state Björn Drews, ..., Johannes Hecker Denschlag (2016)

Exploring inelastic and reactive collisions on the quantum level is a main goal of the developing field of ultracold chemistry. We present first experimental studies of inelastic collisions of metastable ultracold triplet molecules in the vibrational ground state. The measurements are performed with nonpolar $\textrm{Rb}_2$ dimers which are prepared in precisely-defined quantum states and trapped in an array of quasi-1D potential tubes. In particular, we investigate collisions of molecules in the absolute lowest triplet energy level where any inelastic process requires a change of the electronic state. Nevertheless, we find similar decay rates as for collisions between rotationally or vibrationally excited triplet molecules and they are close to the rates for universal reactions. As anticipated theoretically, the measured decay rate constants vary considerably when confinement and collision energy are changed. This might be exploited to control the collisional properties of molecules.

The discussed paper presents experimental studies of inelastic collisions of metastable ultracold triplet Rb2 molecules in the vibrational ground state, focusing on decay rates and control through confinement and collision energy. However, the abstract and selected parts do not specifically mention microwave shielding or the explicit use of external electric or magnetic fields to modulate the collision rates. While the subject of controlling molecular collision properties is related, the primary focus of microwave-induced rotational state dressing and its interaction with external fields is not addressed.

 🔴 [64]
Feshbach spectroscopy and dual-species Bose-Einstein condensation of $^{23}\mathrm{Na}-$$^{39}\mathrm{K}$ mixtures Torben A. Schulze, ..., Silke Ospelkaus (2017)

We present measurements of interspecies Feshbach resonances and subsequent creation of dual-species Bose-Einstein condensates of $^{23}\mathrm{Na}$ and $^{39}\mathrm{K}$. We prepare both optically trapped ensembles in the spin state $\left|f = 1,m_{f}=-1\right\rangle$ and perform atom loss spectroscopy in a magnetic field range from 0 to $700 \, \mathrm{G}$. The observed features include several s-wave poles and a zero crossing of the interspecies scattering length as well as inelastic two-body contributions in the $\mathcal{M} = m_{\mathrm{Na}}+m_{\mathrm{K}} = -2$ submanifold. We identify and discuss the suitability of different magnetic field regions for the purposes of sympathetic cooling of \K and achieving dual-species degeneracy. Two condensates are created simultaneously by evaporation at a magnetic field of about $150 \, \mathrm{G}$, which provides sizable intra- and interspecies scattering rates needed for fast thermalization. The impact of the differential gravitational sag on the miscibility criterion for the mixture is discussed. Our results serve as a promising starting point for the magnetoassociation into quantum degenerate $^{23}\mathrm{Na}^{39}\mathrm{K}$ Feshbach molecules.

This paper focuses on the characterization of interspecies Feshbach resonances, including observations of Feshbach resonances, interaction zeroes, and channel mixing in Na-K mixtures along with the creation of Na-K Bose-Einstein condensates. However, there is no mention or focus on the implementation or effects of microwave shielding to manipulate inelastic collision rates. The paper primarily deals with magnetic field manipulation and does not explore the modification of interaction potentials through microwave-induced rotational state dressing. Thus, while the paper discusses related areas such as resonance properties and interspecies interactions, it does not address the specific concept of microwave shielding and its impact on inelastic collision rates.

 🔴 [65]
Control of reactive collisions by quantum interference Hyungmok Son, ..., Wolfgang Ketterle (2021)

In this study, we achieved magnetic control of reactive scattering in an ultracold mixture of $^{23}$Na atoms and $^{23}$Na$^{6}$Li molecules. In most molecular collisions, particles react or are lost near short range with unity probability, leading to the so-called universal rate. By contrast, the Na{+}NaLi system was shown to have only $\sim4\%$ loss probability in a fully spin-polarized state. By controlling the phase of the scattering wave function via a Feshbach resonance, we modified the loss rate by more than a factor of $100$, from far below to far above the universal limit. The results are explained in analogy with an optical Fabry-Perot resonator by interference of reflections at short and long range. Our work demonstrates quantum control of chemistry by magnetic fields with the full dynamic range predicted by our models.

The abstract describes the control of reactive collisions in a system of sodium atoms and sodium-lithium molecules using magnetic fields, not microwave radiation. The focus here is on the use of magnetic fields and Feshbach resonances to influence the loss rate in collisions; there is no mention of microwave radiation or the dressing of rotational states in bialkali molecules. While the work involves quantum control and collision manipulation, which are related fields, it does not specifically address the desired topic of microwave shielding to mitigate inelastic collisions in bialkali molecules.

 🔴 [66]
Modeling sympathetic cooling of molecules by ultracold atoms Jongseok Lim, ..., M. R. Tarbutt (2015)

We model sympathetic cooling of ground-state CaF molecules by ultracold Li and Rb atoms. The molecules are moving in a microwave trap, while the atoms are trapped magnetically. We calculate the differential elastic cross sections for CaF-Li and CaF-Rb collisions, using model Lennard-Jones potentials adjusted to give typical values for the s-wave scattering length. Together with trajectory calculations, these differential cross sections are used to simulate the cooling of the molecules, the heating of the atoms, and the loss of atoms from the trap. We show that a hard-sphere collision model based on an energy-dependent momentum transport cross section accurately predicts the molecule cooling rate but underestimates the rates of atom heating and loss. Our simulations suggest that Rb is a more effective coolant than Li for ground-state molecules, and that the cooling dynamics are less sensitive to the exact value of the s-wave scattering length when Rb is used. Using realistic experimental parameters, we find that molecules can be sympathetically cooled to 100$\mu$K in about 10s. By applying evaporative cooling to the atoms, the cooling rate can be increased and the final temperature of the molecules can be reduced to 1$\mu$K within 30s.

The selected paper primarily describes modeling of sympathetic cooling involving CaF molecules and Li or Rb atoms in a microwave trap. While it mentions the use of a microwave trap to contain polar molecules in their ground state, thereby leading to feasible sympathetic cooling, it does not focus on bialkali molecules or the specific manipulation of their inelastic collision rates through microwave shielding in the presence of external fields. Furthermore, the emphasis is on cooling rates and trap loss rather than the direct control of inelastic collision rates in bialkali molecules.

 🔴 [67]
Collisions of ultracold molecules in bright and dark optical dipole traps Roman Bause, ..., Xin-Yu Luo (2021)

Understanding collisions between ultracold molecules is crucial for making stable molecular quantum gases and harnessing their rich internal degrees of freedom for quantum engineering. Transient complexes can strongly influence collisional physics, but in the ultracold regime, key aspects of their behavior have remained unknown. To explain experimentally observed loss of ground-state molecules from optical dipole traps, it was recently proposed that molecular complexes can be lost due to photo-excitation. By trapping molecules in a repulsive box potential using laser light near a narrow molecular transition, we are able to test this hypothesis with light intensities three orders of magnitude lower than what is typical in red-detuned dipole traps. This allows us to investigate light-induced collisional loss in a gas of nonreactive fermionic $^{23}$Na$^{40}$K molecules. Even for the lowest intensities available in our experiment, our results are consistent with universal loss, meaning unit loss probability inside the short-range interaction potential. Our findings disagree by at least two orders of magnitude with latest theoretical predictions, showing that crucial aspects of molecular collisions are not yet understood, and provide a benchmark for the development of new theories.

The paper discusses collisions of ultracold molecules in optical dipole traps and focuses on observed molecular loss, specifically in the context of NaK molecules. There is a mention of using microwave pulses to create a coherent superposition of ground-state samples and its subsequent decoherence, as well as the effects of the trap light and electric fields on the collision rate. While this is related to the manipulation of molecular states and trapping conditions, it is not specifically about microwave shielding aimed at reducing inelastic collision rates of bialkali molecules. The emphasis seems to be on understanding collisional losses rather than using microwaves to control the collision rates. Therefore, it does not appear to focus directly on the specific desired topic, as it does not address the role of microwave fields in shielding bialkali molecules against inelastic collisions in the presence of external electric or magnetic fields.

 🔴 [68]
Manipulation of Molecules with Electromagnetic Fields Mikhail Lemeshko, ..., Sabre Kais (2013)

The goal of the present article is to review the major developments that have led to the current understanding of molecule-field interactions and experimental methods for manipulating molecules with electromagnetic fields. Molecule-field interactions are at the core of several, seemingly distinct, areas of molecular physics. This is reflected in the organization of this article, which includes sections on Field control of molecular beams, External field traps for cold molecules, Control of molecular orientation and molecular alignment, Manipulation of molecules by non-conservative forces, Ultracold molecules and ultracold chemistry, Controlled many-body phenomena, Entanglement of molecules and dipole arrays, and Stability of molecular systems in high-frequency super-intense laser fields. The article contains 853 references.

The paper titled 'Manipulation of Molecules with Electromagnetic Fields' provides a review of molecule-field interactions and details various experimental methods for handling molecules with electromagnetic fields. Specifically, it discusses the sensitivity of molecular collisions to external electric and magnetic fields, how these fields affect rotational structures, and the induction of scattering resonances. Though the paper references control of molecular interactions through external fields and highlights the universality of scattering properties in strong dipole-dipole interactions, these aspects only tangentially relate to the topic of interest. There is no clear discussion about the use of microwave shielding itself to modify interaction potentials drastically and its exact effect on the inelastic collision rate of bialkali molecules.

 🔴 [69]
Cold molecules: Progress in Quantum Engineering of Chemistry and Quantum Matter John L Bohn, ..., Jun Ye (2017)

Cooling atoms to ultralow temperatures has produced a wealth of opportunities in fundamental physics, precision metrology, and quantum science. The more recent application of sophisticated cooling techniques to molecules, which has been more challenging to implement due to the complexity of molecular structures, has now opened door to the longstanding goal of precisely controlling molecular internal and external degrees of freedom and the resulting interaction processes. This line of research can leverage fundamental insights into how molecules interact and evolve to enable the control of reaction chemistry and the design and realization of a range of advanced quantum materials.

The provided paper discusses the advancements in controlling the degrees of freedom and interactions in cold molecules, including creating polar molecular chains and clusters using microwave dressing. It touches on the stabilization of certain molecular structures using microwave fields and highlights experimental progress with bialkali molecules. However, the abstract does not mention the target topic - specifically how microwave fields affect the inelastic collision rate of bialkali molecules in the presence of external fields. While it is relevant to the broader context of molecular physics and might provide useful background information, the paper's focus does not appear to be on the specific topic of interest regarding the interaction of microwave fields with external fields to modify bialkali molecules' collision rates.

 🔴 [70]
Sisyphus Cooling of Electrically Trapped Polyatomic Molecules M. Zeppenfeld, ..., G. Rempe (2012)

The rich internal structure and long-range dipole-dipole interactions establish polar molecules as unique instruments for quantum-controlled applications and fundamental investigations. Their potential fully unfolds at ultracold temperatures, where a plethora of effects is predicted in many-body physics, quantum information science, ultracold chemistry, and physics beyond the standard model. These objectives have inspired the development of a wide range of methods to produce cold molecular ensembles. However, cooling polyatomic molecules to ultracold temperatures has until now seemed intractable. Here we report on the experimental realization of opto-electrical cooling, a paradigm-changing cooling and accumulation method for polar molecules. Its key attribute is the removal of a large fraction of a molecule's kinetic energy in each step of the cooling cycle via a Sisyphus effect, allowing cooling with only few dissipative decay processes. We demonstrate its potential by reducing the temperature of about 10^6 trapped CH_3F molecules by a factor of 13.5, with the phase-space density increased by a factor of 29 or a factor of 70 discounting trap losses. In contrast to other cooling mechanisms, our scheme proceeds in a trap, cools in all three dimensions, and works for a large variety of polar molecules. With no fundamental temperature limit anticipated down to the photon-recoil temperature in the nanokelvin range, our method eliminates the primary hurdle in producing ultracold polyatomic molecules. The low temperatures, large molecule numbers and long trapping times up to 27 s will allow an interaction-dominated regime to be attained, enabling collision studies and investigation of evaporative cooling toward a BEC of polyatomic molecules.

While the paper examines the cooling and trapping of polyatomic molecules rather than bialkali molecules, it does explore electric trapping and the use of microwaves in conjunction with electric fields to manipulate molecular internal states and potentials. Though the specific focus of the paper is not on inelastic collision rates or bialkali molecules, the techniques used could be conceptually related to the area of interest. Nevertheless, the paper's primary outcome is to achieve cooling, and the study of inelastic collisions is not its objective. Therefore, it could provide auxiliary or background insight, but it doesn't directly address the core topic.

 🔴 [71]
Reactions Between Layer-Resolved Molecules Mediated by Dipolar Exchange William G. Tobias, ..., Jun Ye (2021)

Microscopic control over polar molecules with tunable interactions would enable realization of novel quantum phenomena. Using an applied electric field gradient, we demonstrate layer-resolved state preparation and imaging of ultracold potassium-rubidium molecules confined to two-dimensional planes in an optical lattice. The coherence time of rotational superpositions in individual layers is maximized by rotating the electric field relative to the optical trap polarization to achieve state-insensitive trapping. Molecules in adjacent layers interact via dipolar exchange of rotational angular momentum; by adjusting the interaction strength between spatially separated ensembles of molecules, we regulate the local chemical reaction rate. The observed resonance width of the exchange process vastly exceeds the dipolar interaction energy, an effect we attribute to the thermal energy. This work realizes precise control of interacting molecules, enabling electric field microscopy on subwavelength length scales and allowing access to unexplored physics in two-dimensional systems.

The paper discusses the microscopic control of polar potassium-rubidium molecules in a state-dependent trapping environment using an electric field gradient. While this indicates a focus on electric field manipulation of polar molecules to tune interactions and regulate chemical reactions, it does not explicitly mention microwave shielding or the drastic change of inelastic collision rates due to such shielding in the presence of electric or magnetic fields other than the interaction adjustments within a 2D optical lattice set up. Therefore, the specific topic of investigating microwave-induced modification of interaction potentials and inelastic collision rates in bialkali molecules seems to be tangentially related or not directly addressed by this paper.

 🔴 [72]
High density loading and collisional loss of laser cooled molecules in an optical trap Varun Jorapur, ..., David DeMille (2023)

We report optical trapping of laser-cooled molecules at sufficient density to observe molecule-molecule collisions for the first time in a bulk gas. SrF molecules from a red-detuned magneto-optical trap (MOT) are compressed and cooled in a blue-detuned MOT. Roughly 30% of these molecules are loaded into an optical dipole trap with peak number density $n_0 \approx 3\times 10^{10} \text{ cm}^{-3}$ and temperature $T\approx40$ $\mu$K. We observe two-body loss with rate coefficient $\beta = 2.7^{+1.2}_{-0.8}\times 10^{-10} \text{ cm}^3 \text{ s}^{-1}$. Achieving this density and temperature opens a path to evaporative cooling towards quantum degeneracy of laser-cooled molecules.

The paper discusses the loading and collisional loss of laser-cooled molecules in an optical trap, specifically SrF molecules, which do not fall into the category of bialkali molecules of interest (e.g., KRb, RbCs, NaK, NaCs). The specifics of microwave shielding are indeed mentioned, but primarily in the context of bi-alkali molecules in a different experimental set-up: molecules at much lower temperatures and different methods (using microwave fields or static electric fields) were referenced only in passing to highlight the possibility of collisional cooling. Moreover, there is no explicit mention of the influence of external electric or magnetic fields on the inelastic collision rates of the bialkali molecules, or the drastic change thereof due to these fields, which is the main focus of your research.

 🔴 [73]
Microwave coherent control of ultracold ground-state molecules formed by short-range photoassociation Zhonghua Ji, ..., Suotang Jia (2020)

We report the observation of microwave coherent control of rotational states of ultracold $^{85}$Rb$^{133}$Cs molecules formed in their vibronic ground state by short-range photoassociation. Molecules are formed in the single rotational state $X(v=0,J=1)$ by exciting pairs of atoms to the short-range state $(2)^{3}\Pi_{0^{-}} (v=11, J=0)$, followed by spontaneous decay. We use depletion spectroscopy to record the dynamic evolution of the population distribution and observe clear Rabi oscillations while irradiating on a microwave transition between coupled neighbouring rotational levels. A density-matrix formalism that accounts for longitudinal and transverse decay times reproduces both the dynamic evolution during the coherent process and the equilibrium population. The coherent control reported here is valuable both for investigating coherent quantum effects and for applications of cold polar molecules produced by continuous short-range photoassociation.

The paper presents an observation of microwave-induced control over the rotational states of ultracold RbCs molecules, a relevant bialkali system. However, it focuses on the coherent control and measurement of the molecules using microwave fields, rather than discussing the specific effect of such control on inelastic collision rates in the presence of external fields. While related to microwave control of bialkali molecules, this paper does not address the conceptual core of the desired topic: the drastic change in inelastic collision rates due to the presence of an external field. The paper's significance is centered on coherent control achieved through irradiation, and it lacks the exploration of collision dynamics or the effects of external fields on these dynamics, which are critical to fulfilling your research objective.

 🔴 [74]
Characterization of the lowest excited-state ro-vibrational level of $^{23}$Na$^{87}$Rb Junyu He, ..., Dajun Wang (2021)

Starting from an ultracold sample of ground-state $^{23}$Na$^{87}$Rb molecules, we investigate the lowest ro-vibrational level of the $b^3\Pi$ state with high resolution laser spectroscopy. This electronic spin-forbidden $X^1\Sigma^+ \leftrightarrow b^3\Pi$ transition features a nearly diagonal Franck-Condon factor and has been proposed useful for probing and manipulating the ultracold molecular gas. We measure the transition strength directly by probing the ac Stark shift induced by near resonance light and determine the total excited-state spontaneous emission rate by observing the loss of molecules. From the extracted branching ratio and the theoretical modeling, we find that the leakage to the continuum of the $a^3\Sigma^+$ state plays the dominant role in the total transition linewidth. Based on these results, we show that it is feasible to create optical trapping potentials for maximizing the rotational coherence with laser light tuned to near this transition.

This paper focuses on the spectroscopic characterization of low excited-state ro-vibrational levels in a specific bialkali molecule, 23Na87Rb, rather than on the actual mechanism of microwave shielding to control collision rates. Though it discusses the internal structures of polar molecules and touches upon rotational levels being affected by microwaves, the primary context is about probing and manipulating ultracold molecular gases in general. Importantly, it does not specifically address the use of external electric or magnetic fields in combination with microwaves to influence inelastic collision rates. As such, while related to bialkali molecule manipulation, it does not specifically explore microwave shielding within the parameters of an electric or a magnetic field affecting collision dynamics.

 🔴 [75]
Efficient Creation of Ultracold Ground State $^{6}\textrm{Li}^{40}\textrm{K}$ Polar Molecules Canming He, ..., Kai Dieckmann (2023)

We report the creation of ultracold ground state $^{6}\textrm{Li}^{40}\textrm{K}$ polar molecules with high efficiency. Starting from weakly-bound molecules state, stimulated Raman adiabatic passage (STIRAP) is adopted to coherently transfer the molecules to their singlet ro-vibrational ground state $|\textrm{X}^{1}\Sigma^{+},v=0,J=0>$. By employing a singlet STIRAP pathway and low-phase-noise narrow-linewidth lasers, we observed a one-way transfer efficiency of 96(4)\,\%. Held in an optical dipole trap, the lifetime of the ground-state molecules is measured to be 5.0(3)\,ms. The large permanent dipole moment of LiK is confirmed by applying a DC electric field on the molecules and performing Stark shift spectroscopy of the ground state. With recent advances in the quantum control of collisions, our work paves the way for exploring quantum many-body physics with strongly-interacting $^{6}\textrm{Li}^{40}\textrm{K}$ molecules.

The article discusses the coherent transfer of $^{6}\textrm{Li}^{40}\textrm{K}$ molecules to their ground state, and their properties, including the suppression of inelastic collisional losses. While there is mention of microwave dressing as a method for inelastic loss suppression and enhancement of molecule lifetime within the broader context of bialkali species, the focus of the paper is predominantly on STIRAP for efficient transfer to the ground state. The specific topic of interest which deals with microwave shielding and its effects in the presence of external fields is not the central theme of the research conducted in this article.

 🔴 [76]
Dipolar Collisions of Ultracold Ground-state Bosonic Molecules Mingyang Guo, ..., Dajun Wang (2018)

The dipolar collision between ultracold polar molecules is an important topic both by its own right from the fundamental point of view and for the successful exploration of many-body physics with strong and long-range dipolar interactions. Here, we report the investigation of collisions between ultracold ground-state sodium-rubidium molecules in electric fields with induced electric dipole moments as large as 0.7$\;$D. We observe a step-wise enhancement of losses due to the coupling between different partial waves induced by the increasingly stronger anisotropic dipolar interactions. Varying the temperature of our sample, we find good agreement with theoretical loss rates assuming complex formation as the main loss process. Our results shed new light on the understanding of complex molecular collisions in the presence of strong dipolar interactions and also demonstrate the versatility of modifying molecular interactions with electric fields.

While the study discusses the impact of electric fields on the collisions of ultracold ground-state sodium-rubidium molecules (a type of bialkali molecule), and hence touches on aspects related to the interaction potential and its control, there is no explicit mention of the use of microwave fields for 'dressing' the rotational states of the molecules, as required by the researcher's topic. Additionally, the paper seems to focus more on studying the dipolar interactions in the context of many-body physics rather than specifically addressing changes in the inelastic collision rates due to external electric or magnetic fields, or the use of microwave shielding.

 🔴 [77]
Cavity QED in a molecular ion trap D. I. Schuster, ..., R. J. Schoelkopf (2009)

We propose an approach for studying quantum information and performing high resolution spectroscopy of rotational states of trapped molecular ions using an on-chip superconducting microwave resonator. Molecular ions have several advantages over neutral molecules. Ions can be loaded into deep (1 eV) RF traps and are trapped independent of the electric dipole moment of their rotational transition. Their charge protects them from motional dephasing and prevents collisional loss, allowing 1 s coherence times when used as a quantum memory, with detection of single molecules possible in <10 ms. An analysis of the detection efficiency and coherence properties of the molecules is presented.

The paper describes the use of a superconducting microwave resonator within a molecular ion trap, focusing on quantum information and spectroscopy rather than on modifying collision rates of neutral bialkali molecules via external fields and microwave shielding. It explores the applications of molecular ions, which inherently exhibit different behavior from neutral molecules due to charging, focusing on realizing cavity QED. Although the paper has implications for understanding molecular control and coherence in ion traps, it doesn’t address the specific topic of microwave shielding to affect inelastic collision rates of neutral bialkali molecules in the presence of external electric or magnetic fields.

 🔴 [78]
Extending rotational coherence of interacting polar molecules in a spin-decoupled magic trap Frauke Seeßelberg, ..., Christoph Gohle (2018)

Superpositions of rotational states in polar molecules induce strong, long-range dipolar interactions. Here we extend the rotational coherence by nearly one order of magnitude to 8.7(6) ms in a dilute gas of polar $^{23}$Na$^{40}$K molecules in an optical trap. We demonstrate spin-decoupled magic trapping, which cancels first-order and reduces second-order differential light shifts. The latter is achieved with a dc electric field that decouples nuclear spin, rotation and trapping light field. We observe density-dependent coherence times, which can be explained by dipolar interactions in the bulk gas.

The article focuses on extending the rotational coherence of NaK polar molecules in an optical trap using a combination of a dc electric field and microwave fields. This setup does contribute effectively to controlling the interaction between molecules, which could ultimately influence their inelastic collision rates. However, the paper does not explicitly discuss the drastic alteration of inelastic collision rates in the presence of microwave shielding. It seems more centered on coherence times and their density dependence, potentially implying but not directly addressing the inelastic collision rates of the molecules.

 🔴 [79]
Two-photon optical shielding of collisions between ultracold polar molecules Charbel Karam, ..., Olivier Dulieu (2022)

We propose a method to engineer repulsive long-range interactions between ultracold ground-state molecules using optical fields, thus preventing short-range collisional losses. It maps the microwave coupling recently used for collisional shielding onto a two-photon transition, and takes advantage of optical control techniques. In contrast to one-photon optical shielding [Phys. Rev. Lett. 125, 153202 (2020)], this scheme avoids heating of the molecular gas due to photon scattering. The proposed protocol, exemplified for 23Na39K, should be applicable to a large class of polar diatomic molecules.

The paper discusses the use of two-photon optical shielding as a method to reduce collisional losses by engineering repulsive long-range interactions in ultracold ground-state molecules, with an emphasis on 23Na39K which is a bialkali molecule. Although it employs optical fields rather than microwave radiation, the underlying principle of modifying intermolecular interactions to prevent inelastic collisions is closely related. However, the specific focus on optical rather than microwave methods and the absence of an electric or magnetic field in the paper's method suggest it does not directly address the exact topic of interest involving microwave shielding in the presence of external fields.

 🔴 [80]
Elastic and inelastic collisions of $^2Σ$ molecules in a magnetic field Jie Cui, ..., Roman V. Krems (2013)

We calculate the cross sections for elastic scattering and Zeeman relaxation in binary collisions of molecules in the ro-vibrational ground state of a $^2\Sigma$ electronic state and the Zeeman state with the electron spin projection $M_S=1/2$ on the magnetic field axis. This is the lowest-energy state of $^2\Sigma$ molecules confined in a magnetic trap. The results are averaged over calculations with multiple molecule - molecule interaction potentials, which yields the expectation intervals for the cross sections and the elastic-to-inelastic cross section ratios. We find that the elastic-to-inelastic cross section ratios under conditions corresponding to trapped molecular ensembles at $T \sim 10^{-3}$ K exceed 100 for the majority of $^2\Sigma$ molecules. The range of $^2\Sigma$ molecules expected to be collisionally unstable in magnetic traps at $T < 10^{-3}$ K is limited to molecules with the spin-rotation interaction constant $\gamma_{\rm SR} > 0.5$ cm$^{-1}$ and the rotational constant $B_e < 4$ cm$^{-1}$.

The paper discusses $^2\Sigma$ molecules in magnetic fields, focusing on elastic scattering and Zeeman relaxation. It calculates cross-sections for collisions but does not mention the use of microwave fields nor bialkali molecules specifically. Although the subject is related to molecular behavior under magnetic influence, it does not cover microwave shielding or the bialkali molecules that the researcher is interested in, nor does it deal with the change of inelastic collision rate by external fields other than magnetism.

 🔴 [81]
Second-Scale Nuclear Spin Coherence Time of Trapped Ultracold $^{23}$Na$^{40}$K Molecules Jee Woo Park, ..., Martin W. Zwierlein (2016)

Coherence, the stability of the relative phase between quantum states, lies at the heart of quantum mechanics. Applications such as precision measurement, interferometry, and quantum computation are enabled by physical systems that have quantum states with robust coherence. With the creation of molecular ensembles at sub-$\mu$K temperatures, diatomic molecules have become a novel system under full quantum control. Here, we report on the observation of stable coherence between a pair of nuclear spin states of ultracold fermionic NaK molecules in the singlet rovibrational ground state. Employing microwave fields, we perform Ramsey spectroscopy and observe coherence times on the scale of one second. This work opens the door for the exploration of single molecules as a versatile quantum memory. Switchable long-range interactions between dipolar molecules can further enable two-qubit gates, allowing quantum storage and processing in the same physical system. Within the observed coherence time, $10^4$ one- and two-qubit gate operations will be feasible.

The paper presented focuses on the coherence between nuclear spin states in ultracold NaK molecules, where microwave fields are applied for state coupling and control. It reports on the observation of long coherence times. While this paper demonstrates control of molecular states using microwave fields, it does not specifically address the use of microwave shielding in the presence of external fields to drastically change the inelastic collision rate in bialkali molecules. The microwave fields are used for state coupling rather than for the modification of interaction potential, and there is no mention of external electric or magnetic field being utilized to this end. Thus, the paper does not directly contribute to the understanding of interaction potential modification via microwave fields to influence inelastic collision rates.

 🔴 [82]
Robust Coherent Control of Bimolecular Collisions beyond the Ultracold Regime Adrien Devolder, ..., Timur Tscherbul (2023)

Quantum coherent control of bimolecular collisions beyond the ultracold regime can face a major challenge due to the incoherent addition of different partial wave contributions to the total scattering cross section. These contributions become increasingly numerous as the collision energy increases, leading to a loss of overall control. Here, we overcome this limitation by leveraging the recently discovered Partial Wave Phase Locking (PWPL) effect, which synchronizes the oscillations of all partial wave contributions. By using rigorous quantum scattering calculations, we demonstrate that PWPL enables coherent control of spin exchange in ion-atom collisions, far outside the ultracold regime, even with as many as 5000 partial wave contributions. The predicted extent of control is sufficient to be measurable in cold atom-ion hybrid experiments.

This paper focuses on the coherent control of bimolecular collisions beyond the ultracold regime, employing Partial Wave Phase Locking (PWPL) to synchronize partial wave contributions and control collisions. Although it references research related to microwave shielding of ultracold molecules, it primarily deals with ion-atom collisions and coherent control rather than microwave shielding of bialkali molecules in external fields. The scientific context aligns closely with the broader fields of molecular collisions and quantum control, but there is no clear emphasis on the microwave shielding of bialkali molecules as required by the topic of interest. Additionally, the paper discusses experiments involving 87Rb and 88Sr+, which, while related to one half of a bialkali molecule, does not focus on bialkali molecules themselves.

 🔴 [83]
Collisions Between Ultracold Atoms and Cold Molecules in a Dual Electrostatic-Magnetic Trap N. J. Fitch, ..., H. J. Lewandowski (2020)

Measurements of interactions between cold molecules and ultracold atoms can allow for a detailed understanding of fundamental collision processes. These measurements can be done using various experimental geometries including where both species are in a beam, where one species is trapped, or when both species are trapped. Simultaneous trapping offers significantly longer interaction times and an associated increased sensitivity to rare collision events. However, there are significant practical challenges associated with combining atom and molecule systems, which often have competing experimental requirements. Here, we describe in detail an experimental system that allows for studies of cold collisions between ultracold atoms and cold molecules in a dual trap, where the atoms and molecules are trapped using static magnetic and electric fields, respectively. As a demonstration of the system's capabilities, we study cold collisions between ammonia ($^{14}$ND$_{3}$ and $^{15}$ND$_{3}$) molecules and rubidium ($^{87}$Rb and $^{85}$Rb) atoms.

Although the article by N. J. Fitch et al. discusses collisions between cold molecules (ammonia) and ultracold atoms (rubidium) in a trap using static electric and magnetic fields, it does not specifically address the topic of microwave shielding for bialkali molecules. The focus is on the measurement of cold collisions and the characterization of an experimental setup rather than the control of inelastic collision rates through microwave dressing. Additionally, the paper does not mention the use of external microwave fields to modify bialkali molecule interactions or a drastic change in inelastic collision rates.

 🔴 [84]
Ultracold Dipolar Gas of Fermionic $^{23}$Na$^{40}$K Molecules in their Absolute Ground State Jee Woo Park, ..., Martin W. Zwierlein (2015)

We report on the creation of an ultracold dipolar gas of fermionic $^{23}$Na$^{40}$K molecules in their absolute rovibrational and hyperfine ground state. Starting from weakly bound Feshbach molecules, we demonstrate hyperfine resolved two-photon transfer into the singlet ${\rm X}^1\Sigma^+ |v{=}0,J{=}0\rangle$ ground state, coherently bridging a binding energy difference of 0.65 eV via stimulated rapid adiabatic passage. The spin-polarized, nearly quantum degenerate molecular gas displays a lifetime longer than 2.5 s, highlighting NaK's stability against two-body chemical reactions. A homogeneous electric field is applied to induce a dipole moment of up to 0.8 Debye. With these advances, the exploration of many-body physics with strongly dipolar Fermi gases of $^{23}$Na$^{40}$K molecules is in experimental reach.

The paper presents the production of ultracold dipolar gases of NaK molecules and their transfer into the ground state, highlighting the stability of these molecules against two-body chemical reactions. The use of STIRAP and electric field application to induce a dipole moment is discussed. However, it does not specifically address the use of microwave shielding techniques to modify the inelastic collision rates of bialkali molecules in the presence of external electric or magnetic fields. The focus instead lies on the production, ground state transfer and dipolar induction, which are foundational but only tangentially related to the specific topic of microwave shielding and its impact on collision rates.

 🔴 [85]
Coherent Microwave Control of Ultracold $^{23}$Na$^{40}$K Molecules Sebastian A. Will, ..., Martin W. Zwierlein (2016)

We demonstrate coherent microwave control of rotational and hyperfine states of trapped, ultracold, and chemically stable $^{23}$Na$^{40}$K molecules. Starting with all molecules in the absolute rovibrational and hyperfine ground state, we study rotational transitions in combined magnetic and electric fields and explain the rich hyperfine structure. Following the transfer of the entire molecular ensemble into a single hyperfine level of the first rotationally excited state, $J{=}1$, we observe collisional lifetimes of more than $3\, \rm s$, comparable to those in the rovibrational ground state, $J{=}0$. Long-lived ensembles and full quantum state control are prerequisites for the use of ultracold molecules in quantum simulation, precision measurements and quantum information processing.

The paper discusses coherent microwave control of ultracold sodium-potassium (a bialkali molecule) and investigates rotational transitions in a combination of magnetic and electric fields. It demonstrates prolonged collisional lifetimes in the rotationally excited state due to microwave control, implying an effect on inelastic collision rates. However, the article does not explicitly mention the shielding effects of microwave fields nor a drastic change in inelastic collision rates. The research might be peripherally relevant, as it highlights control over internal states affecting collisional properties, but it may not focus specifically on the desired topic of 'microwave shielding' and the 'drastic' change in such rates.

 🔴 [86]
Ion-assisted ground-state cooling of a trapped polar molecule Zbigniew Idziaszek, ..., Peter Zoller (2010)