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modulation transfer spectroscopy's implementation in laser locking

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I would like to know experiment conducted on atomic vapor with details about the generation of the error signal and the electronic circuits


Deep search found 13 relevant papers. This is ~99% of all relevant papers that exist on the arXiv database (see comprehensiveness analysis for details).

Highly Relevant References
 🟢 [1]
Sub-Doppler modulation spectroscopy of potassium for laser stabilization L. Mudarikwa, ..., J. Goldwin (2011)

We study modulation spectroscopy of the potassium D2 transitions at 766.7 nm. The vapour pressure, controlled by heating a commercial reference cell, is optimized using conventional saturated absorption spectroscopy. Subsequent heterodyne detection yields sub-Doppler frequency discriminants suitable for stabilizing lasers in experiments with cold atoms. Comparisons are made between spectra obtained by direct modulation of the probe beam, and those using modulation transfer from the pump via nonlinear mixing. Finally, suggestions are made for further optimization of the signals.

The paper clearly describes the implementation of modulation transfer spectroscopy in laser stabilization. It provides an experimental setup that discusses phase modulation of the pump and probe beams, generation of the probe sidebands, and heterodyne detection for obtaining frequency discriminants. It also discusses directly locking to a saturated absorption peak and the undesirable sensitivity this method has to fluctuations in optical power, vapour pressure, and offset voltage. Some electronic components and circuits involved in this setup are mentioned, as well as opportunities for optimizing the signals. Thus, this paper seems highly relevant to the desired topic.

 🟢 [2]
Simultaneous modulation transfer spectroscopy on transitions of multiple atomic species for compact laser frequency reference modules Moritz Mihm, ..., Patrick Windpassinger (2018)

We present a technique for simultaneous laser frequency stabilization on transitions of multiple atomic species with a single optical setup. The method is based on modulation transfer spectroscopy and the signals are separated by modulating at different frequencies and electronically filtered. As a proof of concept, we demonstrate simultaneous spectroscopy of the potassium D$_1$, D$_2$ and rubidium D$_2$ transitions. The technique can easily be extended to other atomic species and allows the development of versatile and compact frequency reference modules.

The paper presents a technique that uses modulation transfer spectroscopy for laser frequency stabilization in multiple atomic species. Importantly, it also details how error signals are generated and separated for different atomic species using electronic filtering. The experimental setup described in the paper seems to be closely related to the desired topic's focus on atomic vapor and the generation of error signals.

 🟢 [3]
Modulation transfer spectroscopy in atomic rubidium D. J. McCarron, ..., S. L. Cornish (2008)

We report modulation transfer spectroscopy on the D2 transitions in 85Rb and 87Rb using a simple home-built electro-optic modulator (EOM). We show that both the gradient and amplitude of modulation transfer spectroscopy signals, for the 87Rb F=2 to F'=3 and the 85Rb F=3 to F'=4 transitions, can be significantly enhanced by expanding the beams, improving the signals for laser frequency stabilization. The signal gradient for these transitions is increased by a factor of 3 and the peak to peak amplitude was increased by a factor of 2. The modulation transfer signal for the 85Rb F=2 to F' transitions is also presented to highlight how this technique can generate a single, clear line for laser frequency stabilization even in cases where there are a number of closely spaced hyperfine transitions.

This paper indeed discusses the application of modulation transfer spectroscopy on atomic rubidium transitions which is direct implementation in laser locking, as mentioned in the abstract and certain parts of the paper. It also details the generation of the error signal which is used for laser frequency regulation, and describes a simple design for a home-built electro-optic modulator (EOM). However, it doesn't seem to delve deep into the details about the electronic circuits. Nevertheless, this paper provides valuable insights into modulation transfer spectroscopy and its application in laser locking with atomic vapors.

 🟢 [4]
Zeeman-tunable Modulation Transfer Spectroscopy Chloe So, ..., Charles S. Adams (2019)

Active frequency stabilization of a laser to an atomic or molecular resonance underpins many modern-day AMO physics experiments. With a flat background and high signal-to-noise ratio, modulation transfer spectroscopy (MTS) offers an accurate and stable method for laser locking. Despite its benefits, however, the four-wave mixing process that is inherent to the MTS technique entails that the strongest modulation transfer signals are only observed for closed transitions, excluding MTS from numerous applications. Here, we report for the first time the observation of a magnetically tunable MTS error signal. Using a simple two-magnet arrangement, we show that the error signal for the $^{87}$Rb $F=2 \rightarrow F'=3$ cooling transition can be Zeeman-shifted over a range of $>$15 GHz to any arbitrary point on the rubidium $\text{D}_2$ spectrum. Modulation transfer signals for locking to the $^{87}$Rb $F=1 \rightarrow F'=2$ repumping transition as well as 1 GHz red-detuned to the cooling transition are presented to demonstrate the versatility of this technique, which can readily be extended to the locking of Raman and lattice lasers.

The paper clearly discusses MTS and its application in laser locking, as seen in the abstract and the selected parts of the paper. Experiments conducted on the atomic vapor of 87Rb are presented, with an interesting focus on Zeeman tunable MTS error signals. The paper also discusses the electronic circuits used in their experimental setup, complete with modulation and demodulation procedures, suggesting a promising match with the research topic.

 🟢 [5]
Magnetic-enhanced modulation transfer spectroscopy and laser locking for 87Rb repump transition Jin-Bao Long, ..., Jian-Wei Pan (2018)

Locking of a laser frequency to an atomic or molecular resonance line is a key technique in applications of laser spectroscopy and atomic metrology. Modulation transfer spectroscopy (MTS) provides an accurate and stable laser locking method which has been widely used. Normally, the frequency of the MTS signal would drift due to Zeeman shift of the atomic levels and rigorous shielding of stray magnetic field around the vapor cell is required for the accuracy and stability of laser locking. Here on the contrary, by applying a transverse bias magnetic field, we report for the first time observation of a magnetic-enhanced MTS signal on the transition of 87Rb D2-line Fg=1 to Fe=0 (close to the repump transition of Fg=1 to Fe=2), with signal to noise ratio larger than 100:1. The error signal is immune to the external magnetic fluctuation. Compared to the ordinary MTS scheme, it provides a robust and accurate laser locking approach with more stable long-term performance. This technique can be conveniently applied in areas of laser frequency stabilization, laser manipulation of atoms and precision measurement.

The paper's abstract and part of the introduction clearly state the use of Modulation Transfer Spectroscopy (MTS) in locking laser frequency. Particular emphasis on atomic medium (87Rb D2-line) and error signal generation, along with its immunity to external magnetic fluctuation, has been noted. The transverse bias magnetic field implementation offers an alternative method for robust and accurate laser locking. Though it doesn't explicitly describe the electronic circuits in the selected parts, it shows promise in extensively covering them in the full paper due to its experimental nature.

 🟢 [6]
Absolute frequency references at 1529 nm and 1560 nm using modulation transfer spectroscopy Y. Natali Martinez de Escobar, ..., Morgan W. Mitchell (2015)

We demonstrate a double optical frequency reference (1529 nm and 1560 nm) for the telecom C-band using $^{87}$Rb modulation transfer spectroscopy. The two reference frequencies are defined by the 5S$_{1/2} F=2 \rightarrow $ 5P$_{3/2} F'=3$ two-level and 5S$_{1/2} F=2 \rightarrow $ 5P$_{3/2} F'=3 \rightarrow $ 4D$_{5/2} F"=4$ ladder transitions. We examine the sensitivity of the frequency stabilization to probe power and magnetic field fluctuations, calculate its frequency shift due to residual amplitude modulation, and estimate its shift due to gas collisions. The short-term Allan deviation was estimated from the error signal slope for the two transitions. Our scheme provides a simple and high performing system for references at these important wavelengths. We estimate an absolute accuracy of $\sim$ 1 kHz is realistic.

The paper appears to be highly relevant to the stated goal, as it describes the implementation of Modulation Transfer Spectroscopy (MTS) with 87Rb for frequency references at 1529 nm and 1560 nm. Notably, the paper discusses the generation of error signals, the impact of environmental and instrumental factors such as residual amplitude modulation, probe power and magnetic fields on the frequency stabilization. It also hints at electronic circuits through terms like frequency modulation and noise eater. The use of atomic vapor (Rb specifically) is central to the paper. Although the fine details about the electronic circuits are not explicitly laid out in the provided excerpts, the paper seems rich in specific insights into the topic.

 🟢 [7]
Compact 459 nm Cs cell optical frequency standard with $2.1\times{10}^{-13}/\sqrtτ$ short-term stability Jianxiang Miao, ..., Jingbiao Chen (2022)

We achieve a compact optical frequency standard with an extended cavity diode laser locked to the 459 nm 6S$_{1/2}$ - 7P$_{1/2}$ transition of thermal $^{133}$Cs atoms in a $\phi$ 10 mm $\times$ 50 mm glass cell, using modulation transfer spectroscopy (MTS). The self-estimated frequency stability of this laser is $1.4\times{10}^{-14}/\sqrt{\tau}$. With heterodyne measurement, we verify the linewidth-narrowing effect of MTS locking and measure the frequency stability of the locked laser. The linewidth of each laser is reduced from the free-running 69.6 kHz to 10.3 kHz after MTS stabilization, by a factor of 6.75. The Allan deviation measured via beat detection is $2.1\times{10}^{-13}/\sqrt{\tau}$ for each MTS-stabilized laser. In addition, we measure the hyperfine structure of the 7P$_{1/2}$ energy level based on the heterodyne measurements, and calculate the magnetic dipole constant $A$ of the Cs 7P$_{1/2}$ level to be 94.38(6) MHz, which agrees well with previous measurements. This compact optical frequency standard can also be used in other applications that require high-stability lasers, such as laser interferometry, laser cooling, geodesy, and so on.

This paper extensively discusses the use of modulation transfer spectroscopy (MTS) in laser locking, focusing on its implementation to stabilize the frequency of a 459 nm laser locked to a specific transition of 133Cs atoms. The paper not only implements MTS but also measures its effectiveness, suggesting some ways to improve it. Furthermore, notable sections discuss the generation of the error signal and its connection to frequency fluctuations. Therefore, it seems to satisfy most areas of interest defined in the topic, although it seems to lack specific discussions about the electronic circuits involved.

 🟢 [8]
Frequency stabilization of a 739 nm laser to an $I_2$ spectrum for trapped Ytterbium ions Hao Wu, ..., Le Luo (2022)

We report on the frequency stabilization of a 739 nm Ti:sapphire laser to a hyperfine component of the $^{127}I_{2}$ B(1)-X(11) P(70) transition using acousto-optic modulation transfer spectroscopy (MTS). A frequency stability of $3.83\times 10^{-11}$ around 13 s averaging time is achieved when the laser frequency is stabilized. The observed hyperfine transition of the molecular iodine is an ideal frequency reference for locking the lasers used in experiments with trapped ytterbium ions, since its second harmonic frequency is the $^{2}S_{\frac{1}{2}}-^{2}P_{\frac{1}{2}}$ transition of the ytterbium ion at 369.5 nm. By investigating the line broadening effects due to the iodine vapor pressure and laser power, the locking is optimized to the theoretical signal to noise ratio (TSNR) of this iodine transition.

This paper primarily discusses how modulation transfer spectroscopy was used to stabilize the frequency of a 739 nm Ti:Sapphire laser in experiments with trapped Ytterbium ions, using an iodine vapor as the medium. The paper presents the technical details of the setup, including components of the electronic circuits, and highlights some of the practical challenges associated with the approach. Therefore, it corresponds quite well to the topics of interest. Although it does not go into great depth on the generation of the error signal, the paper seems to be very relevant to the specified topics.

 🟢 [9]
Two-color modulation transfer spectroscopy A. Perez Galvan, ..., Y. Zhao (2008)

We present two-color modulation transfer spectroscopy as a tool for precision studies of atomic properties of excited states. The bi-colored technique addresses a narrow set of velocity groups of a thermal atomic vapour using a two-step transition to "burn a hole" in the velocity distribution. The resulting spectrum presents sub-Doppler linewidths, good signal to noise ratio and the trademark sidebands that work as an in situ ruler for the energy spacing between atomic resonances. The spectra obtained can be used for different applications such as measurements of energy splittings or stabilization of laser frequencies to excited atomic transitions.

This paper appears to detail an experiment involving atomic vapor (87Rb), and speaks specifically about the use of modulation transfer spectroscopy in stabilizing laser frequencies. It discusses the interaction of the lasers and the generation of the error signal, also providing insight into the methods and circuits used to lock the lasers. Specifically, it mentions the locking of the probe laser to the 5P3/2 → 5D5/2 excited atomic resonance and achieving a reduction of noise. The modulation of the pump and probe lasers and the effects of these modulations on the excited state atomic resonances are clearly outlined. This paper seems to thoroughly address the desired topic with a focus on atomic vapor, the generation of the error signal, and electronic circuits, which are of specific interest to the researcher.

Closely Related References
 🟡 [10]
Wideband laser locking to an atomic reference with modulation transfer spectroscopy Vlad Negnevitsky, ..., Lincoln D. Turner (2012)

We demonstrate that conventional modulated spectroscopy apparatus, used for laser frequency stabilization in many atomic physics laboratories, can be enhanced to provide a wideband lock delivering deep suppression of frequency noise across the acoustic range. Using an acousto-optic modulator driven with an agile oscillator, we show that wideband frequency modulation of the pump laser in modulation transfer spectroscopy produces the unique single lock-point spectrum previously demonstrated with electro-optic phase modulation. We achieve a laser lock with 100 kHz feedback bandwidth, limited by our laser control electronics. This bandwidth is sufficient to reduce frequency noise by 30 dB across the acoustic range and narrows the imputed linewidth by a factor of five.

In this paper, the authors discuss applying Modulation Transfer Spectroscopy for laser frequency stabilization and highlight the use of an acousto-optic modulator and an agile oscillator for wideband frequency modulation, which seems to align with the desired topic. They also mention achieving a laser lock sufficient enough reduce frequency noise, which indirectly implies the use of an error signal and electronic circuits. However, it is uncertain from the abstract whether the paper goes into extensive detail regarding the generation of error signal and electronic circuits as needed.

 🟡 [11]
Optimization strategies for modulation transfer spectroscopy applied to laser stabilization Tilman Preuschoff, ..., Gerhard Birkl (2020)

We present a general analysis for determining the optimal modulation parameters for the modulation transfer spectroscopy scheme. The results are universally valid and can be applied to spectroscopy of any atomic species requiring only the knowledge of the effective linewidth $\Gamma_{eff}$. A signal with optimized slope and amplitude is predicted for a large modulation index $M$ and a modulation frequency comparable to the natural linewidth of the spectroscopic transition. As a result of competing practical considerations, a modulation index in the range of $3 \le M \le 10$ has been identified as optimal. This parameter regime is experimentally accessible with a setup based on an acousto-optic modulator. An optimized signal for spectroscopy of the rubidium D2 line is presented. The signal shape and the dependence on the modulation parameters are in very good agreement with the theoretical description given. An experimental procedure for achieving a strong suppression of residual amplitude modulation is presented. Based on the optimized signal, we demonstrate long-term laser stabilization resulting in a laser linewidth of 150\,kHz (16\,s average) and a frequency stability of 18\,kHz (rms) over 15 hours.

This paper presents a detailed investigation on optimum modulation parameters for MTS, and how it is used for laser stabilization. It also discusses an experimental setup based on an acousto-optic modulator, indicating an exploration of practical implementation. Moreover, it implements its findings on the rubidium D2 line, which is an example of atomic vapor. However, it does not go in-depth regarding the generation of the error signal and the associated electronic circuits, which is a component the colleague is interested in.

 🟡 [12]
Laser frequency stabilization by combining modulation transfer and frequency modulation spectroscopy Fei Zi, ..., Holger Mueller (2017)

We present a hybrid laser frequency stabilization method combining modulation transfer spectroscopy (MTS) and frequency modulation spectroscopy (FMS) for the cesium D2 transition. In a typical pump-probe setup, the error signal is a combination of the DC-coupled MTS error signal and the AC-coupled FMS error signal. This combines the long-term stability of the former with the high signal-to-noise ratio of the latter. In addition, we enhance the long-term frequency stability with laser intensity stabilization. By measuring the frequency difference between two independent hybrid spectroscopies, we investigate the short-term and long-term stability. We find a long-term stability of 7.8 kHz characterized by a standard deviation of the beating frequency drift over the course of 10 hours, and a short-term stability of 1.9 kHz characterized by an Allan deviation of that at 2 seconds of integration time.

The article titled 'Laser frequency stabilization by combining modulation transfer and frequency modulation spectroscopy' appears to be highly relevant to the desired topic. It explicitly discusses a hybrid approach for laser frequency stability using modulation transfer spectroscopy and frequency modulation spectroscopy. The paper describes the generation of the error signal—the combination of DC-coupled MTS and AC-coupled FMS error signal. However, the reference to electronic circuits used in the process is not readily apparent from the sections provided. Further detail might be present within the main text of the paper which is not available here.

 🟡 [13]
Absolute Te$_2$ reference for barium ion at $455.4~$nm T. Dutta, ..., M. Mukherjee (2016)

Precision atomic spectroscopy is presently the work horse in quantum information technology, metrology, trace analysis and even for fundamental tests in physics. Stable lasers are inherent part of precision spectroscopy which in turn requires absolute wavelength markers suitably placed corresponding to the atomic species being probed. Here we present, new lines of tellurium (Te$_2$) which allows locking of external cavity diode laser (ECDL) for precision spectroscopy of singly charged barium ions. In addition, we have developed an ECDL with over 100 GHz mod-hop-free tuning range using commercially available diode from $\textit{Nichia}$. These two developments allow nearly drift-free operation of a barium ion trap set-up with one single reference cell thereby reducing the complexity of the experiment.

The paper presents an experiment implementing modulation transfer spectroscopy for precision spectroscopy of barium ions. It discusses the development of an external cavity diode laser with a wide tuning range and the use of tellurium as a reference. Additionally, the paper seems to briefly touch on the generation of a zero-crossing signal at the resonance frequency, which hints towards the generation of an error signal. However, it doesn't discuss the electronic circuits involved in detail.

Distantly Related References (missing key criteria)
 🔴 [14]
Invited Review: Micro-fabricated components for cold atom sensors J. P. McGilligan, ..., E. Riis (2022)

Laser cooled atoms have proven transformative for precision metrology, playing a pivotal role in state-of-the-art clocks and interferometers, and having the potential to provide a step-change in our modern technological capabilities. To successfully explore their full potential, laser cooling platforms must be translated from the laboratory environment and into portable, compact quantum sensors for deployment in practical applications. This transition requires the amalgamation of a wide range of components and expertise if an unambiguously chip-scale cold atom sensor is to be realized. We present recent developments in cold-atom sensor miniaturization, focusing on key components that enable laser cooling on the chip-scale. The design, fabrication and impact of the components on sensor scalability and performance will be discussed with an outlook to the next generation of chip-scale cold atom devices.

While I must acknowledge that this article does touch upon the topic of laser stabilization and modulation, it seems the focus is on saturation spectroscopy, rather than modulation transfer spectroscopy. It discusses atomic absorption profiles and their use in laser wavelength locking, and briefly touches ideas of frequency modulation and error signals. But it lacks any detail on modulation transfer spectroscopy as such. It seems more focused on the broader aspects of laser cooling and atomic vapor cell fabrication.

 🔴 [15]
Polarization spectroscopy and magnetically-induced dichroism of the potassium D2 lines K. Pahwa, ..., J. Goldwin (2012)

We study modulation-free methods for producing sub-Doppler, dispersive line shapes for laser stabilization near the potassium D2 transitions at 767 nm. Polarization spectroscopy is performed and a comparison is made between the use of a mirror or beam splitter for aligning the counter-propagating pump and probe beams. Conventional magnetically-induced dichroism is found to suffer from a small dispersion and large background offset. We therefore introduce a modified scheme, using two spatially separated pump-probe beam pairs. Finally we compare our results to methods using phase modulation and heterodyne detection.

The paper clearly talks about the implementation of polarization spectroscopy and magnetically induced dichroism for laser stabilization, specifically with potassium D2 transitions. It indeed talks about atomic spectroscopy error signals and methods to produce them, even briefly discussing modulation transfer spectroscopy. However, the focus of the paper is not exclusively on modulation transfer spectroscopy but also on polarization spectroscopy and modified setup for magnetic dichroism. Therefore, the paper is definitely of scientific relevance to the topic but does not singularly focus on modulation transfer spectroscopy's implementation in laser locking.

 🔴 [16]
Carrier frequency modulation of an acousto-optic modulator for laser stabilization Matthew Aldous, ..., Matt Himsworth (2017)

The stabilization of lasers to absolute frequency references is a fundamental requirement in several areas of atomic, molecular and optical physics. A range of techniques are available to produce a suitable reference onto which one can 'lock' the laser, many of which depend on the specific internal structure of the reference or are sensitive to laser intensity noise. We present a novel method using the frequency modulation of an acousto-optic modulator's carrier (drive) signal to generate two spatially separated beams, with a frequency difference of only a few MHz. These beams are used to probe a narrow absorption feature and the difference in their detected signals leads to a dispersion-like feature suitable for wavelength stabilization of a diode laser. This simple and versatile method only requires a narrow absorption line and is therefore suitable for both atomic and cavity based stabilization schemes. To demonstrate the suitability of this method we lock an external cavity diode laser near the $^{85}\mathrm{Rb}\,5S_{1/2}\rightarrow5P_{3/2}, F=3\rightarrow F^{\prime}=4$ using sub-Doppler pump probe spectroscopy and also demonstrate excellent agreement between the measured signal and a theoretical model.

The presented paper discusses a method for stabilizing lasers that is based on frequency modulation of an acousto-optic modulator's carrier signal, which can be understood as a variety of modulation transfer spectroscopy. The laser stabilization featured in the paper is demonstrated using rubidium as an atomic medium, aligning with the colleague's interest in atomic vapor. The paper however does not provide explicit details on the generation of the error signal and electronic circuits. While it might contribute to the understanding of the overall context, it seems not to delve into the specifics the colleague is interested in.

 🔴 [17]
External Cavity Diode Laser Setup with Two Interference Filters Alexander Martin, ..., Gerhard Birkl (2016)

We present an external cavity diode laser setup using two identical, commercially available interference filters operated in the blue wavelength range around 450 nm. The combination of the two filters decreases the transmission width, while increasing the edge steepness without a significant reduction in peak transmittance. Due to the broad spectral transmission of such interference filters compared to the internal mode spacing of blue laser diodes, an additional locking scheme, based on H\"ansch-Couillaud locking to a cavity, has been added to improve the stability. The laser is stabilized to a line in the tellurium spectrum via saturation spectroscopy, and single-frequency operation for a duration of two days is demonstrated by monitoring the error signal of the lock and the piezo drive compensating the length change of the external resonator due to air pressure variations. Additionally, transmission curves of the filters and the spectra of a sample of diodes are given.

While the paper presents a setup for stabilizing laser frequencies and generating an error signal, it mainly centres on the use of a dual-filter external cavity diode laser, stabilized via Doppler-free saturation spectroscopy to a line in tellurium. Although an error signal is mentioned in the context of the stabilization scheme, the specifics on how it is generated, or the detailed functioning of the associated electronic circuit, are not explicitly discussed in depth. Furthermore, the experiment is not conducted on atomic vapor but on tellurium. The principles of modulation transfer spectroscopy that could relate to their locking system are not directly mentioned.

 🔴 [18]
Laser frequency stabilization to highly excited state transitions using electromagnetically induced transparency in a cascade system R. P. Abel, ..., C. S. Adams (2008)

We demonstrate laser frequency stabilization to excited state transitions using cascade electromagnetically induced transparency (EIT). Using a room temperature Rb vapor cell as a reference, we stabilize a first diode laser to the D2 transition and a second laser to a transition from the intermediate state to a Rydberg state with principal quantum number n=19 - 70. A combined laser linewidth of 280 kHz over a 0.1 ms time period is achieved. This method may be applied generally to any cascade system and allows laser stabilization to an atomic reference in the absence of strong optical transitions.

While this paper does touch on modulation transfer spectroscopy (MTS) and its use in generating an error signal for laser stabilization, it does so in the context of laser stabilization to excited state transitions using electromagnetically induced transparency (EIT) in a cascade system. Of particular note, it mentions that the probe beam is modulated to give sidebands above and below the EIT resonance, generating a detector signal at the modulation frequency - an important aspect of MTS. However, the main focus of the paper appears to be the introduction and application of a new technique for stabilizing lasers to transitions with small A-coefficients, specifically applied to Rydberg states. While it provides some practical use of MTS in an interesting context, the details on the generation of the error signal and the electronic circuits may not be as extensive or explicit as the colleague would desire for their specific topic.

 🔴 [19]
Modulation-free pump-probe spectroscopy of strontium atoms C. Javaux, ..., M. P. A. Jones (2009)

We have performed polarization spectroscopy and sub-Doppler DAVLL on the (5s5s) 1^S_0 -> (5s5p) 1^P_1 transition of atomic strontium. Both techniques generated a dispersion-type lineshape suitable for laser stabilization, without the need for frequency modulation. In both cases the signal is generated primarily by saturation effects, rather than optical pumping. The dependence of the amplitude and gradient on intensity and magnetic field were also investigated.

This paper talks about the laser locking process, including the generation of an error signal; however, it discusses the use of modulation-free pump-probe spectroscopy for this process, rather than modulation transfer spectroscopy. Thus, it does not address the specific method that the researcher is interested in. The paper does provide information about laser frequency stabilization and the error signal generation, which are relevant, but without the context of modulation transfer spectroscopy, this information may not be directly useful for the researcher's goal.

 🔴 [20]
Simultaneous two-photon resonant optical laser locking (STROLLing) in the hyperfine Paschen--Back regime Renju S. Mathew, ..., Ifan G. Hughes (2018)

We demonstrate a technique to lock simultaneously two laser frequencies to each step of a two-photon transition in the presence of a magnetic field sufficiently large to gain access to the hyperfine Paschen-Back regime. A ladder configuration with the 5S$_{1/2}$, 5P$_{3/2}$ and 5D$_{5/2}$ terms in a thermal vapour of $^{87}$Rb atoms is used. The two lasers remain locked for more than 24 hours. For the sum of the laser frequencies, which represents the stability of the two-photon lock, we measure a frequency instability of less than the Rb D$_2$ natural linewidth of 6 MHz for nearly all measured time scales

While this paper indeed focuses on the topic of laser locking, the main method discussed is the simultaneous two-photon resonant optical laser locking, rather than specifically Modulation Transfer Spectroscopy. Although MTS is mentioned, it doesn't seem to be the primary focus of the paper. Furthermore, the paper falls short on providing detailed information regarding the generation of the error signal or discussion related to electronic circuits. Therefore, it may not provide much highlighted information on your specific topic interest.

 🔴 [21]
Low-drift Zeeman shifted atomic frequency reference D. J. Reed, ..., K. J. Weatherill (2018)

We present a simple method for producing a low-drift atomic frequency reference based upon the Zeeman effect. Our Zeeman Shifted Atomic Reference `ZSAR' is demonstrated to have tens of GHz tuning range, limited only by the strength of the applied field. ZSAR uses Doppler-free laser spectroscopy in a thermal vapor where the vapor is situated in a large, static and controllable magnetic field. We use a heated $^{85}$Rb vapor cell between a pair of position-adjustable permanent magnets capable of applying magnetic fields up to 1 T. To demonstrate the frequency reference we use a spectral feature from the Zeeman shifted D1 line in $^{85}$Rb at 795 nm to stabilize a laser to the 7S$_{1/2}$ $\longrightarrow$ 23P$_{1/2}$ transition in atomic cesium, which is detuned by approximately 19 GHz from the unperturbed Rb transition. We place an upper bound on the stability of the technique by measuring a 2.5 MHz RMS frequency difference between the two spectral features over a 24 hour period. This versatile method could be adapted easily for use with other atomic species and the tuning range readily increased by applying larger magnetic fields.

The paper 'Low-drift Zeeman shifted atomic frequency reference' introduces a novel method for stabilizing the frequency of lasers using the Zeeman effect in rubidium vapor. The paper certainly focuses on laser locking, which aligns with the primary area of interest. However, while the paper does utilize saturated absorption and frequency modulation spectroscopy, it does not specifically mention modulation transfer spectroscopy. Furthermore, the paper does not particularly delve into the details of error signal generation or the electronic circuits involved. Thus, while the paper provides a different approach to laser locking, it does not provide specific details that align with the exact focus of your research topic.

 🔴 [22]
Harnessing speckle for a sub-femtometre resolved broadband wavemeter and laser stabilization Nikolaus Klaus Metzger, ..., Kishan Dholakia (2017)

The accurate determination and control of the wavelength of light is fundamental to many fields of science. Speckle patterns resulting from the interference of multiple reflections in disordered media are well-known to scramble the information content of light by complex but linear processes. However, these patterns are, in fact, exceptionally rich in information about the illuminating source. We use a fibre-coupled integrating sphere to generate wavelength-dependent speckle patterns, in combination with algorithms based on the transmission matrix method and principal component analysis, to realize a broadband and sensitive wavemeter. We demonstrate sub-femtometre wavelength resolution at a centre wavelength of 780 nm and a broad calibrated measurement range from 488 to 1064 nm. This is comparable with or exceeding the performance of conventional wavemeters. Using this speckle wavemeter as part of a feedback loop, we stabilize a 780 nm diode laser to achieve a linewidth better than 1 MHz.

This paper focuses on the development of a speckle-based wavemeter and its application in the stabilization of a 780 nm diode laser. Although it discusses laser stabilization, it does not specifically mention modulation transfer spectroscopy or conducting experiments on atomic vapor. Critical elements such as the generation of the error signal and the specifics of the electronic circuits, which are central to the topic of interest, are not directly addressed.

 🔴 [23]
A heated vapor cell unit for DAVLL in atomic rubidium Daniel J. McCarron, ..., Simon L. Cornish (2007)

The design and performance of a compact heated vapor cell unit for realizing a dichroic atomic vapor laser lock (DAVLL) for the D2 transitions in atomic rubidium is described. A 5 cm-long vapor cell is placed in a double-solenoid arrangement to produce the required magnetic field; the heat from the solenoid is used to increase the vapor pressure and correspondingly the DAVLL signal. We have characterized experimentally the dependence of important features of the DAVLL signal on magnetic field and cell temperature. For the weaker transitions both the amplitude and gradient of the signal are increased by an order of magnitude.

Although this paper is about a method (Dichroic Atomic Vapor Laser Lock, DAVLL) to stabilize the laser's frequency to atomic transitions, it does not specifically deal with modulation transfer spectroscopy. A substantial part of the paper discusses the design and handling of a heated vapor cell unit to enhance the DAVLL signal in atomic Rubidium, but the principles and mechanisms differ from MTS. While some aspects of the paper might be of interest (e.g., generation of error signals and laser locking), it does not approach the subject through the lens of MTS nor does it touch upon the generation of MTS’s error signal or the electronic circuits typically used in MTS.

 🔴 [24]
A simple, narrow, and robust atomic frequency reference at 993 nm exploiting the rubidium (Rb) $5\mathit{S}_{1/2}$ to $6\mathit{S}_{1/2}$ transition using one-color two-photon excitation Thomas Nieddu, ..., Síle Nic Chormaic (2018)

We experimentally demonstrate a one-color two-photon transition from the $5\mathit{S}_{1/2}$ ground state to the $6\mathit{S}_{1/2}$ excited state in rubidium (Rb) vapor using a continuous wave laser at 993 nm. The Rb vapor contains both isotopes ($^{85}$Rb and $^{87}$Rb) in their natural abundances. The electric dipole allowed transitions are characterized by varying the power and polarization of the excitation laser. Since the optical setup is relatively simple, and the energies of the allowed levels are impervious to stray magnetic fields, this is an attractive choice for a frequency reference at 993 nm, with possible applications in precision measurements and quantum information processing.

This paper discusses a one-color two-photon transition in rubidium (Rb) vapor and explores the locking of laser frequency to the spectroscopic peaks, which corresponds to laser locking. They employ a TEM LaseLock® module for laser frequency stabilization, generating an error signal for lock-in amplification. However, they do not specify whether the technique they used is modulation transfer spectroscopy (MTS). The paper does delve into the practical implications of their polarization and Zeeman shift findings, but does not elaborate in-depth about the electronic circuits involved in the locking process. Thus, while it does involve laser locking with atomic vapor and error signal generation, it veers from the specific topic in not mentioning MTS or detailing the electronic circuitry.

 🔴 [25]
A tunable low-drift laser stabilized to an atomic reference Tobias Leopold, ..., Piet O. Schmidt (2016)

We present a laser system with a linewidth and long-term frequency stability at the 50 kHz level. It is based on a Ti:Sapphire laser emitting radiation at 882 nm which is referenced to an atomic transition. For this, the length of an evacuated transfer cavity is stabilized to a reference laser at 780 nm locked to the $^{85}$Rb D$_2$-line via modulation transfer spectroscopy. Gapless frequency tuning of the spectroscopy laser is realized using the sideband locking technique to the transfer cavity. In this configuration, the linewidth of the spectroscopy laser is derived from the transfer cavity, while the long-term stability is derived from the atomic resonance. Using an optical frequency comb, the frequency stability and linewidth of both lasers are characterized by comparison against an active hydrogen maser frequency standard and an ultra-narrow linewidth laser, respectively. The laser system presented here will be used for spectroscopy of the $1s^{2}2s^{2}2p\ ^{2}P_{1/2} -\ ^{2}P_{3/2}$ transition in sympathetically cooled Ar$^{13+}$ ions at 441nm after frequency doubling.

The paper discusses the locking of a Ti:Sapphire laser to an atomic transition. It uses a transfer cavity for stabilization, which is analogous to the transfer in modulation transfer spectroscopy. The paper does talk about an error signal generation and mention of PI controllers to process the error signals to control the laser frequency, relating to electronic circuits. However, it appears that the specific method used is Pound-Drever-Hall (PDH) and not Modulation Transfer Spectroscopy (MTS), which may make this less directly applicable to the specific topic of interest.

 🔴 [26]
Doppler-free spectroscopy on Cs D$_1$ line with a dual-frequency laser Moustafa Abdel Hafiz, ..., Rodolphe Boudot (2016)

We report on Doppler-free laser spectroscopy in a Cs vapor cell using a dual-frequency laser system tuned on the Cs D$_1$ line. Using counter-propagating beams with crossed linear polarizations, an original sign-reversal of the usual saturated absorption dip and large increase in Doppler-free atomic absorption is observed. This phenomenon is explained by coherent population trapping (CPT) effects. The impact of laser intensity and light polarization on absorption profiles is reported in both single-frequency and dual-frequency regimes. In the latter, frequency stabilization of two diode lasers was performed, yielding a beat-note fractional frequency stability at the level of $3 \times 10^{-12}$ at 1 s averaging time. These performances are about an order of magnitude better than those obtained using a conventional single-frequency saturated absorption scheme.

Firstly, although this paper focuses on Doppler-free laser spectroscopy in a Cs vapor cell which involves the study of lasers and atomic spectra, it does not specifically specify using modulation transfer spectroscopy. Instead, it uses a dual-frequency laser system. Secondly, the paper primarily explores the impact of laser intensity and light polarization on absorption profiles both in single-frequency and dual-frequency regimes, which only touches on part of the researcher's interests. Lastly, although the paper mentions laser frequency stabilization, it does not provide concrete details about the generation of the error signal and the relevant electronic circuits. Encountering coherent population trapping (CPT) effects is interesting but not the primary focus of the researcher's query.

 🔴 [27]
A misaligned magneto-optical trap to enable miniaturized atom chip systems Ritayan Roy, ..., Matt Himsworth (2018)

We describe the application of displaced, or misaligned, beams in a mirror-based magneto-optical trap (MOT) to enable portable and miniaturized atom chip experiments, where optical access is limited to a single window. Two different geometries of beam displacement are investigated: a variation on the well-known 'vortex-MOT', and the other a novel 'hybrid-MOT' combining Zeeman-shifted and purely optical scattering force components. The beam geometry is obtained similar to the mirror-MOT, using a planar mirror surface but with a different magnetic field geometry more suited to planar systems. Using these techniques, we have trapped around 6$\times 10^6$ and 26$\times 10^6$atoms of $^{85}$Rb in the vortex-MOT and hybrid-MOT respectively. For the vortex-MOT the atoms are directly cooled well below the Doppler temperature without any additional sub-Doppler cooling stage, whereas the temperature of the hybrid-MOT has been measured slightly above the Doppler temperature limit. In both cases the attained lower temperature ensures the quantum behaviour of the trapped atoms required for the applications of portable quantum sensors and many others.

While this paper does mention modulation transfer spectroscopy, its main focus is on the development and implementation of misaligned beams in a mirror-based magneto-optical trap (MOT), specifically for miniaturizing atom chip experiments. It also explores cooling and trapping of rubidium atoms, and the creation of novel MOT configurations. The mention of MTS seems to be in passing or as a reference for laser locking, not as an in-depth exploration of its implementation or the associated error signal generation and electronic circuitry.

 🔴 [28]
Laser frequency stabilization using a transfer interferometer Shira Jackson, ..., Amar C. Vutha (2018)

We present a laser frequency stabilization system that uses a transfer interferometer to stabilize slave lasers to a reference laser. Our implementation uses off-the-shelf optical components along with microcontroller-based digital feedback, and offers a simple, flexible and robust way to stabilize multiple laser frequencies to better than 1 MHz.

The paper investigates a method for laser frequency stabilization using a transfer interferometer which is distinct from modulation transfer spectroscopy. Although the paper provides potential insights into laser stabilization and even discusses the generation of an error signal, there's limited focus on atomic vapor or electronic circuits. Importantly, the technique investigated is different from modulation transfer spectroscopy. Therefore, while the paper might provide interesting context and ideas adjacent to the specific interest, it does not directly address the research topic.

 🔴 [29]
Frequency Stabilization of a 369 nm Diode Laser by Nonlinear Spectroscopy of Ytterbium Ions in a Discharge Michael W Lee, ..., Michael J Biercuk (2014)

We demonstrate stabilisation of an ultraviolet diode laser via Doppler free spectroscopy of Ytterbium ions in a discharge. Our technique employs polarization spectroscopy, which produces a natural dispersive lineshape whose zero-crossing is largely immune to environmental drifts, making this signal an ideal absolute frequency reference for Yb$^+$ ion trapping experiments. We stabilise an external-cavity diode laser near 369 nm for cooling Yb$^+$ ions, using amplitude-modulated polarisation spectroscopy and a commercial PID feedback system. We achieve stable, low-drift locking with a standard deviation of measured laser frequency ~400 kHz over 10 minutes, limited by the instantaneous linewidth of the diode laser. These results and the simplicity of our optical setup makes our approach attractive for stabilization of laser sources in atomic-physics applications.

This paper principally discusses the stabilization of a laser frequency using polarization spectroscopy on Ytterbium ions. Although it mentions the modulation transfer spectroscopy (MTS), it doesn't delve into the specific details of utilizing MTS for laser locking. Furthermore, the experiment does not seem to involve atomic vapor, and the paper does not seem to provide significant details about error signal generation or details of the electronic circuit in the context of MTS.

 🔴 [30]
Acetylene-based frequency stabilization of a laser system for potassium laser cooling Charbel Cherfan, ..., Radu Chicireanu (2019)

We demonstrate a laser frequency stabilization technique for laser cooling of Potassium atoms, based on saturated absorption spectroscopy in the C-Band optical telecommunication window, using ro-vibrationel transitions of the acetylene molecule ($12$C$_2$H$_2$). We identified and characterized several molecular lines, which allow to address each of the potassium D2 (767 nm) and D1 (770 nm) cooling transitions, thanks to a high-power second harmonic generation (SHG) stage. We successfully used this laser system to cool the $^{41}$K isotope of potassium in a 2D-3D Magneto-Optical Traps setup.

This paper primarily focuses on laser frequency stabilization using saturated absorption spectroscopy in an acetylene molecular transition, which is different from the modulation transfer spectroscopy technique. However, there are elements of modulation transfer scheme mentioned and implemented for error signal generation, which is of interest in our context. Electronic circuits related details such as high-bandwidth PID module and lock-in amplifier (Toptica DigiLock 110) are mentioned but not in a definitive descriptive manner. The topic of atomic vapor is touched on towards the end of the paper when they mention using a separate saturated absorption potassium, but the paper doesn't centralize its focus on atomic vapors.

 🔴 [31]
High resolution spectroscopy on Te_2: new lines for reference T. Dutta, ..., M. Mukherjee (2018)

Ro-vibrational spectra of different electronic states of molecules are often used as absolute wavelength or frequency standards. These standards are also used to mitigate any slow drift of laser frequency during an experiment. In precision experiment, the two most commonly used molecular standards are iodine and tellurium, both are homo-nuclear diatomic molecules. The former is mostly used as standard for the long wavelength ($600-900$~nm) region, while the tellurium spectrum is widely used in short wavelength ($400-550$~nm) including near ultra violet. A comprehensive data on tellurium spectra can be obtained from the tellurium atlas~\cite{Te2atlas:80}. However near the $455~$nm range where a number of important atomic resonance line, the atlas provides no significant data. We have performed high resolution modulation transfer spectroscopy~(MTS) on tellurium molecule in a hot cell in the region close to $455~$nm wavelength thereby obtained more than $100$ new spectral lines which were not observed before. The resolution of each of these peaks is about few MHz, making them suitable for laser frequency locking.

The paper discusses the use of modulation transfer spectroscopy on tellurium atoms for high resolution. It further outlines the procedure performed, explaining how an error signal's zero-crossing point in the MTS spectrum was used to determine resonance lines, and some circuit elements are briefly mentioned, which play a role in signal processing. Therefore, the paper is relevant to modulation transfer spectroscopy’s implementation in laser locking. However, it does not provide comprehensive details about the generation of the error signal or in-depth about the electronic circuits, these are aspects that are of particular interest to your research.

 🔴 [32]
Vapor-cell frequency reference for short-wavelength transitions in neutral calcium Jennifer Taylor, ..., Steven Peil (2018)

We have characterized the molecular tellurium (Te$_2$) spectrum in the vicinity of the 423nm $^1S_0-^1P_1$ and the 431nm $^3P_1-^3P_0$ transitions in neutral calcium. These transitions are relevant to optical clocks for atomic-beam characterization and cooling (423nm) and enhanced detection (431nm). The use of a Te$_2$ vapor cell as a frequency reference has many advantages over other laser stabilization techniques, and we discuss an application to measuring the instability due to the second-order Doppler shift in a calcium beam clock.

While this paper discusses the challenges and attributes associated with stabilizing laser frequencies (and it does talk about laser locking), it doesn't mention modulation transfer spectroscopy or offer details about the generation of error signal and the specific electronic circuits used. Instead, the focus is on different methods of frequency stabilization, including the use of a vapor cell reference. It discusses vapor-cell usage in laser stabilization techniques for atomic spectra, which can be tied to the general theme of laser locking, but it doesn’t delve into the specifics of modulation transfer spectroscopy in laser locking.

 🔴 [33]
Tellurium Spectrometer for ${}^1\text{S}_0-{}^{1}\text{P}_1$ Transitions in Strontium and Other Alkaline-Earth Atoms T. G. Akin, ..., Steven Peil (2022)

We measure the spectrum of tellurium-130 in the vicinity of the 461~nm ${}^1\text{S}_0-{}^{1}\text{P}_1$ cycling transition in neutral strontium, a popular element for atomic clocks, quantum information, and quantum-degenerate gases. The lack of hyperfine structure in tellurium results in a spectral density of transitions nearly 50 times lower than that available in iodine, making use of tellurium as a laser-frequency reference challenging. By frequency-offset locking two lasers, we generate the large frequency shifts required to span the difference between a tellurium line and the ${}^1\text{S}_0-{}^1\text{P}_1$ resonance in strontium or other alkaline-earth atom. The resulting laser architecture is long-term frequency stable, widely tunable, and optimizes available laser power. The versatility of the system is demonstrated by using it to quickly switch between any strontium isotope in a magneto-optical trap and by adapting it to spectroscopy on a thermal beam with a different alkaline-earth atom.

The paper titled 'Tellurium Spectrometer for ${}^1\text{S}_0-{}^{1}\text{P}_1$ Transitions in Strontium and Other Alkaline-Earth Atoms' uses a different method for laser frequency stabilization - frequency-offset locking instead of modulation transfer spectroscopy. It focuses on an experimental setup with a tellurium spectrometer and discusses the architecture of the laser system, but it does not provide detailed information on the generation of error signals or electronic circuits related to the locking process. The paper is relevant in terms of the broader subject matter (laser frequency stabilization) but does not specifically focus on the topics of MTS and associated circuitry, as the desired topic specifies.

 🔴 [34]
Frequency stabilization of a 650 nm laser to I$_{2}$ spectrum for trapped $^{138}$Ba$^{+}$ ions Tian Xie, ..., Kihwan Kim (2018)

The optical manipulation of Ba$^{+}$ ions is mainly performed by a 493 nm laser for the S$_{1/2}$-P$_{1/2}$ transition and a 650 nm laser for the P$_{1/2}$-D$_{3/2}$ transition. Since the branching ratio between the 493 nm and 650 nm transitions of a single Ba$^{+}$ ion is comparable, stabilization systems of both lasers are equally important for Doppler cooling, sub-Doppler cooling, optical pumping and state detection. The stabilization system of a 493 nm laser to an absolute Te$_2$ reference has been well established. However, the stabilization of a 650 nm laser has not been presented before. Here we report twenty spectral lines of I$_{2}$ in the range of 0.9 GHz above the resonance of the P$_{1/2}$-D$_{3/2}$ transition. We stabilize the 650 nm laser through the optical cavity to the lowest one among these lines, which is about 350 MHz apart, as the absolute frequency reference. Furthermore, we measure the frequency differences between these iodine lines and the Ba$^+$ resonance through fluorescence excitation spectrum with well-resolved dark states, which is in agreement with the theoretical expectation. The presented stabilization scheme enables us to perform precise experiments with Ba$^{+}$ ions.

While this paper revolves around laser frequency stabilization, it specifically explores stabilization to the Iodine spectrum for applications with Barium ions. It details spectrometry and the stabilization system, but the referenced methodology - based on Saturated Absorption Spectroscopy (SAS) and not on modulation transfer spectroscopy. Plus, it doesn't go deeply into the error signal generation or electronic circuits. Therefore, while it's related in terms of laser frequency stabilization, it fails to cover crucial aspects of the exact topic.

 🔴 [35]
A Laser System for the Spectroscopy of Highly-Charged Bismuth Ions S. Albrecht, ..., G. Birkl (2011)

We present and characterize a laser system for the spectroscopy on highly-charged ^209Bi^82+ ions at a wavelength of 243.87 nm. For absolute frequency stabilization, the laser system is locked to a near-infra-red laser stabilized to a rubidium transition line using a transfer cavity based locking scheme. Tuning of the output frequency with high precision is achieved via a tunable rf offset lock. A sample-and-hold technique gives an extended tuning range of several THz in the UV. This scheme is universally applicable to the stabilization of laser systems at wavelengths not directly accessible to atomic or molecular resonances. We determine the frequency accuracy of the laser system using Doppler-free absorption spectroscopy of Te_2 vapour at 488 nm. Scaled to the target wavelength of 244 nm, we achieve a frequency uncertainty of \sigma_{244nm} = 6.14 MHz (one standard deviation) over six days of operation.

This paper discusses a quite complex laser system which is used for spectroscopy on highly charged bismuth ions. It describes tuning and stabilization of a laser using different methods but it does not explicitly mention the use of modulation transfer spectroscopy. Though it contains some relevant aspects like frequency stabilization and tuning, and generation of error signal, these are achieved through methods unrelated to modulation transfer spectroscopy. Despite containing some useful experimental details about laser stabilization techniques at spectrally inaccessible wavelengths, the paper doesn't address atomic vapor usage nor modulation transfer spectroscopy.

 🔴 [36]
A diode laser stabilization scheme for 40Ca+ single ion spectroscopy F. Rohde, ..., J. Eschner (2009)

We present a scheme for stabilizing multiple lasers at wavelengths between 795 and 866 nm to the same atomic reference line. A reference laser at 852 nm is stabilized to the Cs D2 line using a Doppler-free frequency modulation technique. Through transfer cavities, four lasers are stabilized to the relevant atomic transitions in 40Ca+. The rms linewidth of a transfer-locked laser is measured to be 123 kHz with respect to an independent atomic reference, the Rb D1 line. This stability is confirmed by the comparison of an excitation spectrum of a single 40Ca+ ion to an eight-level Bloch equation model. The measured Allan variance of 10^(-22) at 10 s demonstrates a high degree of stability for time scales up to 100 s.

This paper is about stabilizing multiple lasers at different wavelengths to the same atomic reference line using a technique akin to modulation transfer spectroscopy, even if not named as such. The Doppler-free frequency modulation technique used can be considered conceptually similar to MTS as it is also aiming at stabilizing the laser frequency relative to atomic transitions. The paper provides information about both the error signal generation (using the Pound-Drever-Hall technique) and the detailed set-up with elements of their electronic circuits, matching the researcher's context. However, this paper focuses mainly on the Cs D2 line as a reference and not specifically on atomic vapor in a MTS context. Also, it does not directly discuss the consequences of power variations, sensitivity to magnetic fields, or restrictions related to specific atomic transitions

 🔴 [37]
VECSEL systems for generation and manipulation of trapped magnesium ions Shaun C. Burd, ..., David J. Wineland (2016)

Experiments in atomic, molecular, and optical (AMO) physics rely on lasers at many different wavelengths and with varying requirements on spectral linewidth, power, and intensity stability. Vertical external-cavity surface-emitting lasers (VECSELs), when combined with nonlinear frequency conversion, can potentially replace many of the laser systems currently in use. Here we present and characterize VECSEL systems that can perform all laser-based tasks for quantum information processing experiments with trapped magnesium ions. For photoionization of neutral magnesium, 570.6$\,$nm light is generated with an intracavity frequency-doubled VECSEL containing a lithium triborate (LBO) crystal for second harmonic generation. External frequency doubling produces 285.3$\,$nm light for resonant interaction with the $^{1}S_{0}\leftrightarrow$ $^{1}P_{1}$ transition of neutral Mg. Using an externally frequency-quadrupled VECSEL, we implement Doppler cooling of $^{25}$Mg$^{+}$ on the 279.6$\,$nm $^{2}S_{1/2}\leftrightarrow$ $^{2}P_{3/2}$ cycling transition, repumping on the 280.4$\,$nm $^{2}S_{1/2}\leftrightarrow$ $^{2}P_{1/2}$ transition, coherent state manipulation, and resolved sideband cooling close to the motional ground state. Our systems serve as prototypes for applications in AMO requiring single-frequency, power-scalable laser sources at multiple wavelengths.

While this paper touches on laser cooling, ion trapping, and spectroscopy, with some mention of frequency stabilization and error signal generation through locking mechanisms, it doesn't seem to specifically address Modulation Transfer Spectroscopy and its application in laser frequency locking. The main focus of the paper appears to be on vertical external-cavity surface-emitting lasers (VECSELs) and their use in quantum information processing experiments, particularly with trapped magnesium ions.

 🔴 [38]
Two-Photon Dichroic Atomic Vapor Laser Lock Using Electromagnetically Induced Transparency and Absorption F. E. Becerra, ..., L. A. Orozco (2009)

We demonstrate a technique to lock the frequency of a laser to a transition between two excited states in Rb vapor in the presence of a weak magnetic field. We use a ladder configuration from specific hyperfine sublevels of the 5S 1/2, 5P 3/2, and 5D 5/2 levels. This atomic configuration can show Electromagnetically Induced Transparency and Absorption processes. The error signal comes from the difference in the transparency or absorption felt by the two orthogonal polarizations of the probe beam. A simplified model is in good quantitative agreement with the observed signals for the experimental parameters. We have used this technique to lock the frequency of the laser up to 1.5 GHz off atomic resonance.

The presented paper deals primarily with a technique utilized to lock the frequency of a laser in an experiment involving atomic vapor (Rb vapor). It touches upon the generation of an error signal and the mechanisms in the experiment. However, the method explored in the paper does not explicitly employ modulation transfer spectroscopy. Instead, it largely focuses on a new technique based on Dichroic Atomic Vapor Laser Lock (DAVLL), combined with Electromagnetically Induced Transparency and Absorption processes.

 🔴 [39]
Power-efficient frequency switching of a locked laser R. A. Cornelussen, ..., H. B. van Linden van den Heuvell (2003)

We demonstrate a new and efficient laser-locking technique that enables making large frequency jumps while keeping the laser in lock. A diode laser is locked at a variable offset from a Doppler-free spectral feature of rubidium vapor. This is done by frequency shifting the laser before sending the light to a spectroscopy cell with an acousto-optic modulator (AOM). The frequency of the locked laser is switched quasi-instantaneously over much more than the width of the spectral features, i.e. the usual locking range. This is done by simultaneously switching the AOM frequency and applying feed-forward to the laser current. The advantage of our technique is that power loss and beam walk caused by the AOM do not affect the main output beam, but only the small fraction of light used for the spectroscopy. The transient excursions of the laser frequency are only a few MHz and last approximately 0.2 ms, limited by the bandwidth of our locking electronics. We present equations that describe the transient behavior of the error signal and the laser frequency quantitatively. They are in good agreement with the measurements. The technique should be applicable to other types of lasers.

While this paper discusses a new and efficient technique for locking the frequency of a diode laser using Doppler-free saturation spectroscopy in a vapor cell of rubidium, it does not specifically refer to modulation transfer spectroscopy. However, it does go into detail about the generation of error signal and the electronic circuitry involved in the process, which matches some aspects of the specification provided. Therefore, although there is relevance to the larger topic of laser locking, it does not directly address the desired topic of modulation transfer spectroscopy's implementation in laser locking.

 🔴 [40]
Frequency Measurement of an Ar+ Laser Stabilized on Narrow Lines of Molecular Iodine at 501.7 nm Frederic Du Burck, ..., Jean-Pierre Wallerand (2004)

A spectrometer for ultra high-resolution spectroscopy of molecular iodine at wave length 501.7 nm, near the dissociation limit is described. Line shapes about 30 kHz wide (HWHM) were obtained using saturation spectroscopy in a pumped cell. The frequency of an Ar+ laser was locked to a hyperfine component of the R(26)62-0 transition and the first absolute frequency measurement of this line is reported.

The paper discusses the frequency locking of an Ar+ laser by employing saturation spectroscopy in a pumped cell. It includes details about the signal to control the frequency stabilization, involving usage of a narrow-band controller and an adaptive noise cancelling technique. Although it mentions frequency modulation spectroscopy, the method of modulation transfer spectroscopy (MTS) is not explicitly discussed or implemented. Also, there is no emphasis on atomic vapor based experiments or details about electronic circuitry used for MTS. The paper adds a reference about a high-frequency modulation transfer technique but does not provide thorough insight into MTS implementation in the paper itself.

 🔴 [41]
Isotope shifts of natural Sr+ measured by laser fluorescence in a sympathetically cooled Coulomb crystal Brice Dubost, ..., Luca Guidoni (2014)

We measured by laser spectroscopy the isotope shifts between naturally-occurring even-isotopes of strontium ions for both the $5s\,\,^2S_{1/2}\to 5p\,\,^2P_{1/2}$ (violet) and the $4d\,\,^2D_{3/2}\to 5p\,\,^2P_{1/2}$ (infrared) dipole-allowed optical transitions. Fluorescence spectra were taken by simultaneous measurements on a two-component Coulomb crystal in a linear Paul trap containing $10^3$--$10^4$ laser-cooled Sr$^+$ ions. The isotope shifts are extracted from the experimental spectra by fitting the data with the analytical solution of the optical Bloch equations describing a three-level atom in interaction with two laser beams. This technique allowed us to increase the precision with respect to previously reported data obtained by optogalvanic spectroscopy or fast atomic-beam techniques. The results for the $5s\,\,^2S_{1/2}\to 5p\,\,^2P_{1/2}$ transition are $\nu_{88}-\nu_{84}=+378(4)$ MHz and $\nu_{88}-\nu_{86}=+170(3)$ MHz, in agreement with previously reported measurements. In the case of the previously unexplored $4d\,\,^2D_{3/2}\to 5p\,\,^2P_{1/2}$ transition we find $\nu_{88}-\nu_{84}=-828(4)$ MHz and $\nu_{88}-\nu_{86}=-402(2)$ MHz. These results provide more data for stringent tests of theoretical calculations of the isotope shifts of alkali-metal-like atoms. Moreover, they simplify the identification and the addressing of Sr$^+$ isotopes for ion frequency standards or quantum-information-processing applications in the case of multi-isotope ion strings.

The paper mentions the usage of a laser-locking technique involving a frequency-modulation produced by laser-driver electronics. This shares some relation with modulation transfer spectroscopy. However, the paper doesn't detail the process of generating an error signal, nor does it delve into the matter of electronic circuits. The experiments being conducted are also on ionized strontium, which isn't exactly an atomic vapor but shares some experimental similarities. Yet, the paper doesn't heavily focus on this area.

 🔴 [42]
A tunable Doppler-free dichroic lock for laser frequency stabilization Vivek Singh, ..., H. S. Rawat (2016)

We propose and demonstrate a laser frequency stabilization scheme which generates a dispersion-like tunable Doppler-free dichroic lock (TDFDL) signal. This signal offers a wide tuning range for lock point (i.e. zero-crossing) without compromising on the slope of the locking signal. The method involves measurement of magnetically induced dichroism in an atomic vapour for a weak probe laser beam in presence of a counter propagating strong pump laser beam. A simple model is presented to explain the basic principles of this method to generate the TDFDL signal. The spectral shift in the locking signal is achieved by tuning the frequency of the pump beam. The TDFDL signal is shown to be useful for locking the frequency of a cooling laser used for magneto-optcal trap (MOT) for $^{87}Rb$ atoms.

The paper at hand focuses on a laser stabilization scheme, namely a tunable Doppler-free dichroic lock (TDFDL), that uses principles related to modulation transfer spectroscopy: a counter-propagating pump-probe setup with interaction with an atomic vapor. While it does give an insight into a model of the error signal generation and laser locking, it seems not to focus on modulation transfer spectroscopy, as in its core method, but rather an alternate technique. Thus, while elements of the MTS process are present, they are not the main focus. Furthermore, the utilization and details about the specific electronic circuitry aren't discussed.

 🔴 [43]
Atomic frequency reference at 1033 nm for ytterbium (Yb)-doped fiber lasers and applications exploiting a rubidium (Rb) 5$S_{1/2}$ to 4$D_{5/2}$ one-colour two-photon transition Ritayan Roy, ..., Björn Hessmo (2016)

We demonstrate a two-photon transition of rubidium (Rb) atoms from the ground state (5$S_{1/2}$) to the excited state (4$D_{5/2}$), using a home-built ytterbium (Yb)-doped fiber amplifier at 1033 nm. This is the first demonstration of an atomic frequency reference at 1033 nm as well as of a one-colour two-photon transition for the above energy levels. A simple optical setup is presented for the two-photon transition fluorescence spectroscopy, which is useful for frequency stabilization for a broad class of lasers. This spectroscopy has potential applications in the fiber laser industry as a frequency reference, particularly for the Yb-doped fiber lasers. This two-photon transition also has applications in atomic physics as a background- free high- resolution atom detection and for quantum communication, which is outlined in this article.

While the paper discusses aspects of laser frequency stabilization by implementing frequency modulation fluorescence spectroscopy, it does not clearly and directly address the application of modulation transfer spectroscopy (MTS) for laser locking. The error signal generation is discussed but not in the context of MTS. The paper does make reference to the use of certain electronic circuit elements such as the Electro-Optic-Modulator (EOM) and Acousto-Optic Modulator (AOM), alongside some aspects of laser setup. Thus, it has certain relevant components, but deviates in its core subject and methodology from the desired specific topic.

 🔴 [44]
Rydberg-atom based radio-frequency electrometry using frequency modulation spectroscopy in room temperature vapor cells Santosh Kumar, ..., James P. Shaffer (2017)

Rydberg atom-based electrometry enables traceable electric field measurements with high sensitivity over a large frequency range, from gigahertz to terahertz. Such measurements are particularly useful for the calibration of radio frequency and terahertz devices, as well as other applications like near field imaging of electric fields. We utilize frequency modulated spectroscopy with active control of residual amplitude modulation to improve the signal to noise ratio of the optical readout of Rydberg atom-based radio frequency electrometry. Matched filtering of the signal is also implemented. Although we have reached similarly, high sensitivity with other read-out methods, frequency modulated spectroscopy is advantageous because it is well-suited for building a compact, portable sensor. In the current experiment, $\sim 3 \mu V cm^{-1}Hz^{-1/2}$ sensitivity is achieved and is found to be photon shot noise limited.

Although the paper investigates frequency modulated spectroscopy (which is similar to modulation transfer spectroscopy), it does not primarily focus on its application in laser locking. Instead, the researchers implement it for improving the signal to noise ratio in Rydberg-atom based electrometry. While the paper does discuss error signal generation and electronic circuits (like the use of feedback loops to stabilize laser intensity or systems for active compensation of residual amplitude modulation), the context is within the realm of electric field measurements, not laser frequency stabilization or locking.

 🔴 [45]
A versatile, high-power 460nm laser system for Rydberg excitation of ultracold potassium Alda Arias, ..., Shannon Whitlock (2017)

We present a versatile laser system which provides more than 1.5W of narrowband light, tunable in the range from 455-463 nm. It consists of a commercial Titanium-Sapphire laser which is frequency doubled using resonant cavity second harmonic generation and stabilized to an external reference cavity. We demonstrate a wide wavelength tuning range combined with a narrow linewidth and low intensity noise. This laser system is ideally suited for atomic physics experiments such as two-photon excitation of Rydberg states of potassium atoms with principal quantum numbers n > 18. To demonstrate this we perform two-photon spectroscopy on ultracold potassium gases in which we observe an electromagnetically induced transparency resonance corresponding to the 35s1/2 state and verify the long-term stability of the laser system. Additionally, by performing spectroscopy in a magneto-optical trap we observe strong loss features corresponding to the excitation of s, p, d and higher-l states accessible due to a small electric Field.

The paper emphasizes the setup of a high-power laser system for excitation of Rydberg states in potassium. While Modulation Transfer Spectroscopy (MTS) is utilized for locking the laser to the potassium transition, the study does not delve into the detailed process of generating the error signal or the specific electronic circuits associated with MTS. Therefore, it seems the paper may lack the specific in-depth information the researcher is interested in obtaining, especially concerning the electronic circuits associated with MTS.

 🔴 [46]
Frequency locking of tunable diode lasers to a stabilized ring-cavity resonator Ayan Banerjee, ..., Vasant Natarajan (2002)

We demonstrate a technique for locking the frequency of a tunable diode laser to a ring-cavity resonator. The resonator is stabilized to a diode laser which is in turn locked to an atomic transition, thus giving it absolute frequency calibration. The ring-cavity design has the principal advantage that there is no feedback destabilization of the laser. The cavity has a free-spectral range of 1.3 GHz and $Q$ of about 35, which gives robust locking of the laser. The locked laser is able to track large scans of the cavity.

The paper titled 'Frequency locking of tunable diode lasers to a stabilized ring-cavity resonator' does delve into the topic of frequency locking of lasers and mentions the generation of error signals. It demonstrates how a tunable diode laser can be locked to a ring-cavity resonator, which relates to aspects of the laser locking process. Furthermore, it details that the error signal for the locking is obtained by modulating the diodes' injection current and includes information about the electronic circuits used. Also, the setup incorporates the use of an atomic transition. However, the paper does not explicitly address or mention the application of modulation transfer spectroscopy (MTS) in the process. The generation of error signal, an important aspect of MTS, seems to be carried out differently in this study compared to the conventional MTS protocol.

 🔴 [47]
High-performance, compact optical standard Zachary L. Newman, ..., Matthew T. Hummon (2021)

We describe a high-performance, compact optical frequency standard based on a microfabricated Rb vapor cell and a low-noise, external cavity diode laser operating on the Rb two-photon transition at 778 nm. The optical standard achieves an instability of 1.8x10$^{-13}$/$\sqrt{\tau}$ for times less than 100 s and a flicker noise floor of 1x10$^{-14}$ out to 6000 s. At long integration times, the instability is limited by variations in optical probe power and the AC Stark shift. The retrace was measured to 5.7x10$^{-13}$ after 30 hours of dormancy. Such a simple, yet high-performance optical standard could be suitable as an accurate realization of the SI meter or, if coupled with an optical frequency comb, as a compact atomic clock comparable to a hydrogen maser.

The paper's focus is on a high-performance, compact optical standard involving a microfabricated Rb vapor cell and an external cavity diode laser functioning on the Rb two-photon transition. While the paper does extensively discuss optical standards, laser frequency stabilization, and potential sources of instability, it does not explicitly mention modulation transfer spectroscopy. Moreover, it seems that the paper does not provide details concerning the system configuration to generate the error signal or about the electronic circuits used to control the laser's frequency. These topics are central to your research question, hence limiting the relevance of this paper despite its close association with some broad aspects of your inquiry.

 🔴 [48]
A high flux source of cold strontium atoms T. Yang, ..., D. Wilkowski (2015)

We describe an experimental apparatus capable of achieving a high loading rate of strontium atoms in a magneto-optical trap operating in a high vacuum environment. A key innovation of this setup is a two dimensional magneto-optical trap deflector located after a Zeeman slower. We find a loading rate of 6x10^9/s whereas the lifetime of the magnetically trapped atoms in the 3P2 state is 54s.

This paper describes an experimental setup for achieving a high rate of strontium atom loading in a magneto-optical trap in a high vacuum environment. It discusses elements of laser frequency locking and error signal generation, utilizing an Atomic Oven, an Acousto-Optic Modulator (AOM), a photodetector, and a Proportional-Integral-Derivative (PID) controller. However, the study does not specifically focus on the implementation of Modulation Transfer Spectroscopy (MTS), but appears to use transmission spectroscopy for laser stabilization. While the mechanisms discussed are relevant to MTS, they are not specific to it. Furthermore, the paper lacks an in-depth discussion of the electronic circuitry used.

 🔴 [49]
Implementing an electronic sideband offset lock for precision spectroscopy in radium Tenzin Rabga, ..., Jaideep T. Singh (2023)

We demonstrate laser frequency stabilization with at least 6 GHz of offset tunability using an in-phase/quadrature (IQ) modulator to generate electronic sidebands (ESB) on a titanium sapphire laser at 714 nm and we apply this technique to the precision spectroscopy of $^{226}$Ra, and $^{225}$Ra. By locking the laser to a single resonance of a high finesse optical cavity and adjusting the lock offset, we determine the frequency difference between the magneto-optical trap (MOT) transitions in the two isotopes to be $2630.0\pm0.3$ MHz, a factor of 29 more precise than the previously available data. Using the known value of the hyperfine splitting of the $^{3}P_{1}$ level, we calculate the isotope shift for the $^{1}S_{0}$ to $^{3}P_{1}$ transition to be $2267.0\pm2.2$ MHz, which is a factor of 8 more precise than the best available value. Our technique could be applied to countless other atomic systems to provide unprecedented precision in isotope shift spectroscopy and other relative frequency comparisons.

Even though this paper demonstrates a method of laser frequency stabilization, it primarily focuses on the use of an in-phase/quadrature (IQ) modulator to generate electronic sidebands (ESB) for laser spectroscopy, not modulation transfer spectroscopy. Details of the electronic circuits are also lacking. It does not explicitly address modulation transfer spectroscopy nor does it mention locking related to atomic vapor, which is a key part of your research question. Therefore, the topic of the paper is relevant to frequency stabilization in general, but not specifically related to the topic of modulation transfer spectroscopy's implementation in laser locking.

 🔴 [50]
Multi-channel Opto-mechanical Switch and Locking System for Wavemeters Moji Ghadimi, ..., Mirko Lobino (2020)

Here we present a cost effective multi-channel opto-mechanical switch and software PID system for locking multiple lasers to a single channel commercial wavemeter. The switch is based on a rotating cylinder that selectively transmits one laser beam at a time to the wavemeter, the wavelength is read by the computer and an error signal is output to the lasers to correct wavelength drifts every millisecond. We use this system to stabilise 740 nm (subsequently frequency doubled to 370 nm), 399 nm and 935 nm lasers for trapping and cooling different isotopes of Yb+ ion. We characterize the frequency stability of the three lasers by using a second, more precise, commercial wavemeter. We also characterise the absolute frequency stability of the 740 nm laser using the fluorescence drift rate of a trapped 174Yb+ ion. For the 740 nm laser we demonstrate an Allan deviation, df/f, of 3 x 10^-10 (at 20 s integration time), equivalent to sub-200 KHz stability.

While this paper deals with laser locking, it centers around a mechanical switch and software PID system. It does not mention or utilize modulation transfer spectroscopy, which is crucial for the desired topic. The method for generating error signals is mentioned, but not detailed, and the paper's main focus is on frequency stability measurements, not the specific implementation of modulation transfer spectroscopy. In terms of electronic circuits, the paper offers limited specific information.

 🔴 [51]
Manipulation and Detection of a Trapped Yb+ Ion Hyperfine Qubit S. Olmschenk, ..., C. Monroe (2007)

We demonstrate the use of trapped ytterbium ions as quantum bits for quantum information processing. We implement fast, efficient state preparation and state detection of the first-order magnetic field-insensitive hyperfine levels of 171Yb+, with a measured coherence time of 2.5 seconds. The high efficiency and high fidelity of these operations is accomplished through the stabilization and frequency modulation of relevant laser sources.

The provided document discusses in detail the stabilization and frequency modulation of lasers used in quantum information processing with Ytterbium ions. Relevant sections of the paper present a detailed explanation of the electronic and optic setup for laser stabilization and how error signals are generated and utilized, in line with the key desired topic. However, the paper does not specifically refer to modulation transfer spectroscopy, suggesting the technique used might be different or not explicitly identified as such. Additionally, the experiment is conducted on Ytterbium ions, not an atomic vapor.

 🔴 [52]
Coupled Optical Resonance Laser Lockin Shaun Burd, ..., Hermann Uys (2013)

We have demonstrated simultaneous laser frequency stabilization of a UV and IR laser, to the same spectroscopic sample, by monitoring only the absorption of the UV laser. For trapping and cooling Yb$^{+}$ ions, a frequency stabilized laser is required at 369.95nm to drive the $^{2}S_{1/2}$ $ \rightarrow $ $ ^{2}P_{1/2}$ cooling transition. Since the cycle is not closed, a 935.18nm laser is needed to drive the $^{2}D_{3/2}$ $\rightarrow$ $^{3}D_{[3/2]1/2}$ transition which is followed by rapid decay to the $^{2}S_{1/2}$ state. Our 369nm laser is locked to Yb$^{+}$ ions generated in a hollow cathode discharge lamp using saturated absorption spectroscopy. Without pumping, the metastable $^{2}D_{3/2}$ level is only sparsely populated and direct absorption of 935nm light is difficult to detect. A resonant 369nm laser is able to significantly populate the $^{2}D_{3/2}$ state due to the coupling between the levels. Fast re-pumping to the $^{2}S_{1/2}$ state, by 935nm light, can be detected by observing the change in absorption of the 369nm laser using lock-in detection of the photodiode signal. In this way simultaneous locking of two optical frequencies in very different spectral regimes is accomplished. A rate equation model gives good qualitative agreement with the experimental results. This technique offers improved laser frequency stabilization compared to lasers locked individually to the sample and should be readily applicable to similar ion systems.

This paper focuses on a technique for laser frequency stabilization of both a UV and IR laser. It uses Yb+ ions as the spectroscopic sample and discusses the utilization of a rate equation model. However, while the paper talks about using lock-in detection to observe changes, it does not explicitly mention modulation transfer spectroscopy or delve extensively into the details of electronic circuitry or error signal generation in this context. Therefore, I would not classify it as highly relevant to the specific topic of interest.

 🔴 [53]
Current-feedback-stabilized laser system for quantum simulation experiments using Yb clock transition at 578 nm Yoshihiro Takata, ..., Yoshiro Takahashi (2019)

We developed a laser system for the spectroscopy of the clock transition in ytterbium (Yb) atoms at 578 nm based on an interference-filter stabilized external-cavity diode laser (IFDL) emitting at 1156 nm. Owing to the improved frequency-to-current response of the laser-diode chip and the less sensitivity of the IFDL to mechanical perturbations, we succeeded in stabilizing the frequency to a high-finesse ultra-low-expansion glass cavity with a simple current feedback system. Using this laser system, we performed high-resolution clock spectroscopy of Yb and found that the linewidth of the stabilized laser was less than 320 Hz.

Although this paper discusses stabilizing laser frequency using a feedback system for a quantum simulation experiment and deeply explores error signals, oscillation, and response, it does not mention or use modulation transfer spectroscopy as a tool for their laser locking. Thus, this paper does not directly correlate with the exact desired topic. However, parts of the work described, such as relating error signal to stabilizing laser frequency, could indirectly contribute to a broader understanding of the research topic.

 🔴 [54]
Optogalvanic Spectroscopy of Metastable States in Yb^{+} M. J. Petrasiunas, ..., D. Kielpinski (2011)

The metastable ^{2}F_{7/2} and ^{2}D_{3/2} states of Yb^{+} are of interest for applications in metrology and quantum information and also act as dark states in laser cooling. These metastable states are commonly repumped to the ground state via the 638.6 nm ^{2}F_{7/2} -- ^{1}D[5/2]_{5/2} and 935.2 nm ^{2}D_{3/2} -- ^{3}D[3/2]_{1/2} transitions. We have performed optogalvanic spectroscopy of these transitions in Yb^{+} ions generated in a discharge. We measure the pressure broadening coefficient for the 638.6 nm transition to be 70 \pm 10 MHz mbar^{-1}. We place an upper bound of 375 MHz/nucleon on the 638.6 nm isotope splitting and show that our observations are consistent with theory for the hyperfine splitting. Our measurements of the 935.2 nm transition extend those made by Sugiyama et al, showing well-resolved isotope and hyperfine splitting. We obtain high signal to noise, sufficient for laser stabilisation applications.

While the selected paper does touch on some of the aspects of laser locking, it primarily focuses on the use of optogalvanic spectroscopy for laser stabilization rather than modulation transfer spectroscopy. The specific details about the generation of the error signal and the electronic circuits used in modulation transfer spectroscopy are not provided. The method used for laser stabilization in the paper, dichroic atomic vapor laser locking (DAVLL), is different from modulation transfer spectroscopy. While the implementation of a lock-in amplifier is mentioned in the paper, the context does not align with the methodology and details associated with modulation transfer spectroscopy in atomic vapor.

 🔴 [55]
Improved Absolute Frequency Measurement of the 171Yb Optical Lattice Clock at KRISS Relative to the SI Second Huidong Kim, ..., Dai-Hyuk Yu (2017)

We measured the absolute frequency of the $^1S_0$ - $^3P_0$ transition of $^{171}$Yb atoms confined in a one-dimensional optical lattice relative to the SI second. The determined frequency was 518 295 836 590 863.38(57) Hz. The uncertainty was reduced by a factor of 14 compared with our previously reported value in 2013 due to the significant improvements in decreasing the systematic uncertainties. This result is expected to contribute to the determination of a new recommended value for the secondary representations of the second.

The paper discusses the improvement of the absolute frequency of a 171Yb optical lattice clock. It details some methods of stabilizing lasers in this system, such as utilizing frequency combs, lock-ins, and digital servo loops for the optical lattice and the clock laser. It does involve a type of laser locking when working with clock cycles. However, critical components of the specific topic of interest like modulation transfer spectroscopy, error signal generation, and associated electronic circuits are not explicitly mentioned in the provided excerpts. It appears that the paper largely focuses on atomic clocks and their frequency stabilization, not on modulation transfer spectroscopy specifically.

 🔴 [56]
Evidence of Two-Source King Plot Nonlinearity in Spectroscopic Search for New Boson Joonseok Hur, ..., Vladan Vuletić (2022)

Optical precision spectroscopy of isotope shifts can be used to test for new forces beyond the Standard Model, and to determine basic properties of atomic nuclei. We measure isotope shifts on the highly forbidden ${}^2S_{1/2} \rightarrow {}^2F_{7/2}$ octupole transition of trapped $^{168,170,172,174,176}$Yb ions. When combined with previous measurements in Yb$^+$ and very recent measurements in Yb, the data reveal a King plot nonlinearity of up to 240$\sigma$. The trends exhibited by experimental data are explained by nuclear density functional theory calculations with the Fayans functional. We also find, with 4.3$\sigma$ confidence, that there is a second distinct source of nonlinearity, and discuss its possible origin.

From an initial glance at this paper, it seems focused on using precision spectroscopy for the detection of new forces beyond the Standard Model using isotope shifts. While they mention laser locking and using it to stabilize a probe laser to a resonance of a cavity, it is in the context of looking for shifts rather than an in-depth investigation into the laser locking process itself using modulation transfer spectroscopy. Moreover, the topic of modulation transfer spectroscopy is not specified or discussed in detail in the abstract or selected parts of the paper. Also, while electronics and atomic vapors (Yb ions) are mentioned, there isn't explicit information on error signal generation, suggesting this may not be a core focus of the paper.

 🔴 [57]
Optical clock intercomparison with $6\times 10^{-19}$ precision in one hour E. Oelker, ..., J. Ye (2019)

Improvements in atom-light coherence are foundational to progress in quantum information science, quantum optics, and precision metrology. Optical atomic clocks require local oscillators with exceptional optical coherence due to the challenge of performing spectroscopy on their ultra-narrow linewidth clock transitions. Advances in laser stabilization have thus enabled rapid progress in clock precision. A new class of ultrastable lasers based on cryogenic silicon reference cavities has recently demonstrated the longest optical coherence times to date. In this work we utilize such a local oscillator, along with a state-of-the-art frequency comb for coherence transfer, with two Sr optical lattice clocks to achieve an unprecedented level of clock stability. Through an anti-synchronous comparison, the fractional instability of both clocks is assessed to be $4.8\times 10^{-17}/\sqrt{\tau}$ for an averaging time $\tau$ in seconds. Synchronous interrogation reveals a quantum projection noise dominated instability of $3.5(2)\times10^{-17}/\sqrt{\tau}$, resulting in a precision of $5.8(3)\times 10^{-19}$ after a single hour of averaging. The ability to measure sub-$10^{-18}$ level frequency shifts in such short timescales will impact a wide range of applications for clocks in quantum sensing and fundamental physics. For example, this precision allows one to resolve the gravitational red shift from a 1 cm elevation change in only 20 minutes.

While the paper certainly discusses high-precision optics and laser stabilization, it does not specifically study or detail the modulation transfer spectroscopy as a method for laser locking. The paper primarily focuses on the application of these ultrastable lasers in optical atomic clocks and their quantum sensing applications. There is little to no discussion regarding the generation of error signals or the electronic circuits involved in modulation transfer spectroscopy. It seems that their laser locking method involves a digital servo consuming an error signal generated from Rabi spectroscopy, which is rather different from modulation transfer spectroscopy.

 🔴 [58]
Transportable laser system for atom interferometry P. Cheinet, ..., A. Landragin (2005)

We describe an optical bench in which we lock the relative frequencies or phases of a set of three lasers in order to use them in a cold atoms interferometry experiment. As a new feature, the same two lasers serve alternately to cool atoms and to realize the atomic interferometer. This requires a fast change of the optical frequencies over a few GHz. The number of required independent laser sources is then only 3, which enables the construction of the whole laser system on a single transportable optical bench. Recent results obtained with this optical setup are also presented.

Although the paper in question describes an experiment involving laser locks in an atomic interferometry setup, it doesn't specifically address the modulation transfer spectroscopy (MTS). Instead, the described locking scheme relies on FM-Spectroscopy and frequency-to-voltage conversion for locking lasers. There is no explicit mention of MTS, nor is there any detailed discussion around the error signal generation or the circuitry, which is of critical interest to your research. Even though the paper mentions the use of a photodetector and frequency locks, it seems to approach laser locking from a different angle than what is desired.

 🔴 [59]
Observing Quantum Synchronization of a Single Trapped-Ion Qubit Liyun Zhang, ..., Yao Lu (2022)

Synchronizing a few-level quantum system is of fundamental importance to understanding synchronization in deep quantum regime. Whether a two-level system, the smallest quantum system, can be synchronized has been theoretically debated for the past several years. Here, for the first time, we demonstrate that a qubit can indeed be synchronized to an external driving signal by using a trapped-ion system. By engineering fully controllable gain and damping processes, an ion qubit is synchronized to oscillate at the same frequency as the driving signal and lock in phase. We systematically investigate the parameter regions of synchronization and observe characteristic features of the Arnold tongue. Our measurements agree remarkably well with numerical simulations based on recent theory on qubit synchronization. By synchronizing the basic unit of quantum information, our research opens up the possibility of applying quantum synchronization to large-scale quantum networks.

The paper revolves around 'Quantum Synchronization of a Single Trapped-Ion Qubit' and involves the setup of a system that uses a single Ytterbium ion and a laser system. The paper discusses the modulation of the laser via several electro-optic and acoustic-optic modulators to cover all the hyperfine structures of Ytterbium ion, which are some characteristics of modulation transfer spectroscopy. However, the paper does not explicitly mention or focus on modulation transfer spectroscopy, nor does it detail the generation of the error signal or the electronic circuits necessary for this error signal generation. On the other hand, the modulation setup described could potentially be valuable for insights into a related setup for modulation transfer spectroscopy.

 🔴 [60]
The conversion of phase to amplitude fluctuations of a light beam by an optical cavity Alessandro S. Villar (2008)

Very low intensity and phase fluctuations are present in a bright light field such as a laser beam. These subtle quantum fluctuations may be used to encode quantum information. Although intensity is easily measured with common photodetectors, accessing the phase information requires interference experiments. We introduce one such technique, the rotation of the noise ellipse of light, which employs an optical cavity to achieve the conversion of phase to intensity fluctuations. We describe the quantum noise of light and how it can be manipulated by employing an optical resonance technique and compare it to similar techniques, such as Pound-Drever-Hall laser stabilization and homodyne detection.

While this paper discusses frequency stabilization techniques for lasers and mentions the use of phase modulation and an optical cavity to achieve this, it does not specifically talk about Modulation Transfer Spectroscopy (MTS). Its focus is more on the usage of the Pound-Drever-Hall technique and the manipulation of quantum noise of light, which, although related to laser frequency stabilization, diverges from the specific interests of the researcher. Additionally, the paper does not explicitly discuss experiments with atomic vapor or provide much information about the generation of the error signal or the electronic circuits used, which are key points of the researcher's interest.

 🔴 [61]
A phase stable hybrid dual comb spectrometer Sutapa Ghosh, ..., Gadi Eisenstein (2022)

Dual comb spectroscopy (DCS) is a broadband technique offering high resolution and fast data acquisition. We describe a hybrid dual comb spectrometer comprising a broadband commercial fiber laser system offering a wide range of sample interrogation, and an actively mode locked semiconductor laser (MLL) having a widely tunable, relatively narrow spectrum. The mutual coherence over 100 seconds has been realized between the two combs. We employed the DCS system to characterize the absorption spectrum of rubidium atoms at 313 K with a high signal to noise ratio. The broadband laser is directly locked on a high finesse cavity, providing long-term stability, while the semiconductor laser is locked to it. To characterize the absolute stability of the DCS system, the linewidth of the MLL comb line is measured and shown to reduce from 880 kHz to $17$ kHz when the system is fully locked. The long-term stability was measured to be $5 \times 10^{-12}$ at $1$ second and $5 \times 10^{-14}$ at $350$ seconds. The measured timing jitter of the MLL is ten times smaller due to the overall locking. In addition, we have addressed the effect of dispersion on the locking quality, which is significant for broadband comb lasers.

The paper focuses on a method involving dual comb spectroscopy with the use of a commercial laser system and a mode locked semiconductor laser to characterise the absorption spectrum of Rubidium atoms. The paper provides details on how it achieves a stable phase and a high signal to noise ratio. However, it does not mention or appear to involve Modulation Transfer Spectroscopy, nor does it discuss the generation of error signals or electronic circuits in its implementation. Therefore, it seems the paper is not directly relevant to the specific topic of 'modulation transfer spectroscopy's implementation in laser locking'.

 🔴 [62]
Coherent excitation of the highly forbidden electric octupole transition in ${}^{172}$Yb$^+$ Henning A. Fürst, ..., Tanja E. Mehlstäubler (2020)

We report on the first coherent excitation of the highly forbidden $^2S_{1/2}\rightarrow{}^2F_{7/2}$ electric octupole (E3) transition in a single trapped ${}^{172}$Yb$^+$ ion, an isotope without nuclear spin. Using the transition in ${}^{171}$Yb$^+$ as a reference, we determine the transition frequency to be $642\,116\,784\,950\,887.6(2.4)\,$Hz. We map out the magnetic field environment using the forbidden $^2S_{1/2} \rightarrow{}^2D_{5/2}$ electric quadrupole (E2) transition and determine its frequency to be $729\,476\,867\,027\,206.8(4.4)\,$Hz. Our results are a factor of $1\times10^5$ ($3\times10^{5}$) more accurate for the E2 (E3) transition compared to previous measurements. The results open up the way to search for new physics via precise isotope shift measurements and improved tests of local Lorentz invariance using the metastable $^2F_{7/2}$ state of Yb$^+$.

While this paper discusses the coherent excitation of electric octupole transition using lasers and provides some details about laser stabilization, laser frequency tuning, and system set-up, it does not explicitly or extensively discuss the application of Modulation Transfer Spectroscopy (MTS) for the purpose of laser locking. It does mention elements like isotope shifts and the usage of certain equipment that are used in MTS but not explicitly the modulation transfer spectroscopy itself, nor the application within the context of atomic vapor. It also does not delve into the generation of error signals or discuss in detail the electronic circuits associated with MTS. The paper seems more focused on precision measurements and tests of local Lorentz invariance rather than the MTS implementation in laser locking.

 🔴 [63]
Narrow linewidth single laser source system for onboard atom interferometry Fabien Theron, ..., Alexandre Bresson (2014)

A compact and robust laser system for atom interferometry based on a frequency-doubled telecom laser is presented. Thanks to an original stabilization architecture on a saturated absorption setup, we obtain a frequency-agile laser system allowing fast tuning of the laser frequency over 1 GHz in few ms using a single laser source. The different laser frequencies used for atom interferometry are generated by changing dynamically the frequency of the laser and by creating sidebands using a phase modulator. A laser system for Rubidium 87 atom interferometry using only one laser source based on a frequency doubled telecom fiber bench is then built. We take advantage of the maturity of fiber telecom technology to reduce the number of free-space optical components (which are intrinsically less stable) and to make the setup compact and much less sensitive to vibrations and thermal fluctuations. This source provides spectral linewidth below 2.5 kHz, which is required for precision atom interferometry, and particularly for a high performance atomic inertial sensor.

The paper does discuss the topic of laser frequency stabilization, providing detailed descriptions of the laser system and electronic lock. The authors also explain how they generated the error signal, which is amplified, demodulated, low-pass filtered, and finally integrated and amplified to provide a frequency lock. However, the paper appears to focus more on stabilizing the laser for atom interferometry, rather than implementing modulation transfer spectroscopy specifically. There's no explicit mention of modulation transfer spectroscopy, although similar techniques involving phase modulation and lock-in detection are employed. The paper also does not delve deeply into the specifics of the electronic circuits beyond mentioning key components like a phase modulator, a high-voltage amplifier, and a transimpedance amplifier.

 🔴 [64]
A fibered laser system for the MIGA large scale atom interferometer D. O. Sabulsky, ..., B. Canuel (2019)

We describe the realization and characterization of a compact, autonomous fiber laser system that produces the optical frequencies required for laser cooling, trapping, manipulation, and detection of $^{87}$Rb atoms - a typical atomic species for emerging quantum technologies. This device, a customized laser system from the Muquans company, is designed for use in the challenging operating environment of the Laboratoire Souterrain \`{a} Bas Bruit (LSBB) in France, where a new large scale atom interferometer is being constructed underground - the MIGA antenna. The mobile bench comprises four frequency-agile C-band Telecom diode lasers that are frequency doubled to 780 nm after passing through high-power fiber amplifiers. The first laser is frequency stabilized on a saturated absorption signal via lock-in amplification, which serves as an optical frequency reference for the other three lasers via optical phase-locked loops. Power and polarization stability are maintained through a series of custom, flexible micro-optic splitter/combiners that contain polarization optics, acousto-optic modulators, and shutters. Here, we show how the laser system is designed, showcasing qualities such as reliability, stability, remote control, and flexibility, while maintaining the qualities of laboratory equipment. We characterize the laser system by measuring the power, polarization, and frequency stability. We conclude with a demonstration using a cold atom source from the MIGA project and show that this laser system fulfills all requirements for the realization of the antenna.

This article details a sophisticated laser system designed for cooling, trapping, manipulating, and detecting 87Rb atoms in a large scale atom interferometer. It involves laser frequency stabilization using lock-in amplification for a base laser, which then serves as a reference frequency for other lasers. The paper also discusses a servo controller and lock-in amplifier. Despite these, it does not describe or investigate modulation transfer spectroscopy's role in laser locking. Hence, although it relates to laser locking, it omits a key aspect - Modulation Transfer Spectroscopy. Additionally, it doesn't talk about atomic vapor which is another essential component of the desired topic.

 🔴 [65]
A scalable scanning transfer cavity laser stabilization scheme based on the Red Pitaya STEMlab platform Einius Pultinevicius, ..., Tim Langen (2023)

Many experiments in atomic and molecular physics require simultaneous frequency stabilization of multiple lasers. We present a stabilization scheme based on a scanning transfer cavity lock that is simple, stable and easily scalable to many lasers at minimal cost. The scheme is based on the Red Pitaya STEMlab platform, with custom software developed and implemented to achieve up to 100 Hz bandwidth. As an example demonstration, we realize simultaneous stabilization of up to four lasers and a reduction of long-term drifts to well below 1 MHz per hour. This meets typical requirements, e.g. for experiments on laser cooling of molecules.

While there is valuable information in the paper, the core focus is not exactly on the modulation transfer spectroscopy's implementation in laser locking. It’s more concerned with a stabilization scheme for multiple lasers developed using the Red Pitaya STEMlab platform. The paper does reference using an atomic vapor microscopy or a frequency-stable laser as a stabilization reference, but it does not provide extensive details on modulation transfer spectroscopy or the use of electronic circuits for error signal generation. Thus, it does not fully align with the specific topic of interest.

 🔴 [66]
Optical frequency generation using fiber Bragg grating filters for applications in portable quantum sensing C. D. Macrae, ..., M. Holynski (2020)

A method for the agile generation of the optical frequencies required for laser cooling and atom interferometry of rubidium is demonstrated. It relies on fiber Bragg grating technology to filter the output of an electro-optic modulator and was demonstrated in a robust, alignment-free, single-seed, frequency-doubled, telecom fiber laser system. The system was capable of 50 ns frequency switching over a ~40 GHz range, ~0.5 W output power and amplitude modulation with a ~15 ns rise/fall time and an extinction ratio of 120 $\pm$ 2 dB. The technology is ideal for enabling high-bandwidth, mobile industrial and space applications of quantum technologies.

The article appears to discuss the use of modulation transfer spectroscopy (MTS) for the offset frequency lock in an atom interferometry system based on rubidium. It mentions the use of a fiber-coupled MTS setup and a servo controller to maintain the lock. It does not, however, provide a detailed discussion on the formation of the error signal or the exact configuration of the electronic circuits involved in the MTS. The core focus of the paper centers on the agile generation of optical frequencies, using electro-optic modulation and fiber Bragg grating, that are required for laser cooling and atom interferometry.

 🔴 [67]
Direct loading of a large Yb MOT on the $^{1}S_{0} \rightarrow \, ^{3}P_{1}$ transition A Guttridge, ..., S L Cornish (2015)

We report a robust technique for laser frequency stabilisation that enables the reproducible loading of in excess of 10$^{9}$ Yb atoms from a Zeeman slower directly into a magneto-optical trap (MOT) operating on the $^{1}S_{0} \rightarrow \, ^{3}P_{1}$ transition, without the need for a first stage MOT on the $^{1}S_{0} \rightarrow \, ^{1}P_{1}$ transition. We use a simple atomic beam apparatus to generate narrow fluorescence signals on both the 399 nm $^{1}S_{0} \rightarrow \, ^{1}P_{1}$ transition used for the Zeeman slower and the 556 nm $^{1}S_{0} \rightarrow \, ^{3}P_{1}$ transition. We present in detail the methods for obtaining spectra with a high signal-to-noise ratio and demonstrate error signals suitable for robust frequency stabilisation. Finally we demonstrate the stability and precision of our technique through sensitive measurements of the gravitational sag of the Yb MOT as a function of the intensity of the laser cooling beams, which are in good agreement with theory. These results will be important for efficient loading of the atoms into an optical dipole trap.

While this paper does mention laser frequency stabilization and even illustrates error signal generation using a lock-in amplifier, it is clear that the method being used is phase sensitive detection, not Modulation Transfer Spectroscopy. Furthermore, the authors focused heavily on demonstrating their atom-trapping technique for Yb atoms, than on introducing or explaining new designs for the electronic circuits involved with laser locking. In essence, the paper seems more closely tied to atoms manipulation and trapping technique, with laser locking playing more of a complementary role necessary for the research rather than being its core focus. Therefore, while the paper does possess elements related to the desired topic, it does not appear to provide a comprehensive look at MTS or the electronics circuits.

 🔴 [68]
Absolute frequency measurement of the 1S0 - 3P0 transition of 171Yb Marco Pizzocaro, ..., Davide Calonico (2016)

We report the absolute frequency measurement of the unperturbed transition 1S0 - 3P0 at 578 nm in 171Yb realized in an optical lattice frequency standard. The absolute frequency is measured 518 295 836 590 863.55(28) Hz relative to a cryogenic caesium fountain with a fractional uncertainty of 5.4x10-16 . This value is in agreement with the ytterbium frequency recommended as a secondary representation of the second in the International System of Units.

The presented paper focuses on an absolute frequency measurement experiment involving a 171Yb optical lattice frequency standard and does not specifically involve modulation transfer spectroscopy. While the study is concerned with experiments on atomic vapor, the generation of the error signal isn't explicitly discussed, but rather a discussion of laser stability, polarization, trap depth, and frequency controls offered. Also, although it involves laser locking, it doesn't discuss MTS's use in detail. About electronic circuits, only components like the acoustic-optic modulator or double-pass AOM are mentioned vaguely, which doesn't fulfill the researcher's interest in the specifics of electronic circuits involved in MTS context.

 🔴 [69]
Two-beam nonlinear Kerr effect to stabilize laser frequency with sub-Doppler resolution Weliton Soares Martins, ..., Martine. Chevrollier (2012)

Avoiding laser frequency drifts is a key issue in many atomic physics experiments. Several techniques have been developed to lock the laser frequency using sub-Doppler dispersive atomic lineshapes as error signals in a feedback loop. We propose here a two-beam technique that uses non-linear properties of an atomic vapor around sharp resonances to produce sub-Doppler dispersive-like lineshapes that can be used as error signals. Our simple and robust technique has the advantage of not needing either modulation or magnetic fields.

It's vital that we understand that the paper discusses a technique (ANGELLS) for laser frequency locking that does generate a dispersive error signal. However, it is unspecified whether it uses Modulation Transfer Spectroscopy specifically. Several other methods for generating dispersive sub-Doppler signals are mentioned, such as modulation with homodyne detection, but MTS itself isn't stated. Notably, the authors call attention to how their technique avoids using modulation altogether, and this could hint that traditional MTS isn't involved. Lastly, the authors give a brief detail about an electronic circuitry for the feedback control system but do not delve into circuits' schematics deeply.

 🔴 [70]
Magneto-optical polarization rotation in a ladder-type atomic system for tunable offset locking Michał Parniak, ..., Wojciech Wasilewski (2016)

We demonstrate an easily tunable locking scheme for stabilizing frequency-sum of two lasers on a two-photon ladder transition based on polarization rotation in warm rubidium vapors induced by magnetic field and circularly polarized drive field. Unprecedented tunability of the two-photon offset frequency is due to strong splitting and shifting of magnetic states in external field. In our experimental setup we achieve two-photon detuning of up to 700 MHz.

The paper does discuss a method for stabilizing frequencies for lasers, specifically through the use of polarization rotation in rubidium vapors. However, while the paper mentions modulation transfer spectroscopy in passing, it does not seem to be the focus of their method, which instead appears to be a form of magnetic-field induced polarization rotation. Therefore, while relevant to laser locking, it does not specifically focus on modulation transfer spectroscopy and does not provide in-depth coverage of error signal generation or the electronic circuits involved.

 🔴 [71]
Large optical depth frequency modulation spectroscopy Chang Chi Kwong, ..., David Wilkowski (2019)

Band-resolved frequency modulation spectroscopy is a common method to measure weak signals of radiative ensembles. When the optical depth of the medium is large, the signal drops exponentially and the technique becomes ineffective. In this situation, we show that a signal can be recovered when a larger modulation index is applied. Noticeably, this signal can be dominated by the natural linewidth of the resonance, regardless of the presence of inhomogeneous line broadening. We implement this technique on a cesium vapor, and then explore its main spectroscopic features. This work opens the road towards measurement of cooperative emission effects in bulk atomic ensemble.

This paper primarily focuses on large optical depth frequency modulation spectroscopy and its effectiveness when the optical depth of the medium is high. The authors implement the technique on a cesium vapor and explore its spectroscopic features. Although modulation transfer spectroscopy is mentioned in the introduction as a key laser spectroscopic technique, there are no explicit discussions about using modulation transfer spectroscopy for laser locking, the generation of error signals, or details about the specific electronic circuitry involved in the process. Hence, the core focus seems to deviate from the specific research topic our colleague is interested in.

 🔴 [72]
Precision spectroscopy technique for dipole allowed transitions in laser cooled ions Amy Gardner, ..., Matthias Keller (2014)

In this paper we present a technique for the precise measurement of electric dipole allowed transitions in trapped ions. By applying a probe and a cooling laser in quick succession, the full transition can be probed without causing distortion from heating the ion. In addition, two probes can be utilized to measure a dispersion-like signal, which is well suited to stabilizing the laser to the transition. We have fully characterized the parameters for the measurement and find that it is possible to measure the transition frequency to better than 100kHz with an interrogation time of 30s. The long-term stability of the spectroscopy signal is determined by employing two independent ion trap systems. The first ion trap is used to stabilize the spectroscopy laser. The second ion trap is then employed to measure the stability by continuously probing the transition at two frequencies. From the Allan variance a frequency instability of better than 10$^{-10}$ is obtained for an interrogation time of 1000s.

The paper describes a technique for precise measurement of electric dipole allowed transitions in trapped ions through probe and cooling laser. It discusses laser frequency stabilization and the generation of a dispersion-like signal used for this purpose. However, the focus seems more on the stability and precision of spectroscopy signals and does not elaborate on the electronic circuits. The focus is also on trapped ions and it's not clear if atomic vapor was used in this context.

 🔴 [73]
Absolute frequency measurement of the 171Yb optical lattice clock at KRISS using TAI for over a year Huidong Kim, ..., Won-Kyu Lee (2021)

We report a measurement of the absolute frequency of the 1S0-3P0 transition in the 171Yb optical lattice clock at KRISS (KRISS-Yb1) for 14 months, which was referenced to the SI second by primary and secondary standards worldwide via TAI (International Atomic Time). The determined absolute frequency is 518 295 836 590 863.75(14) Hz with the relative frequency uncertainty of 2.6x10^-16, which agrees well with other reports. This result is expected to contribute to the future update of the CIPM recommendation frequency of the secondary frequency standards.

The paper presents an experiment with the 171Yb optical lattice clock where several lasers and modulations are used. This paper discusses the technical details of laser frequency stabilization, and techniques used such as frequency modulations for instance at 29 kHz for better atom transfer. However, even though it includes some aspects of laser locking and modulation, the specific method of modulation transfer spectroscopy (MTS) is not directly discussed to achieve laser frequency locking. Key elements such as interaction of two laser beams (probe and pump), the error signal generation, and the electronic circuits specifically related to MTS are mostly absent.

 🔴 [74]
High-performance frequency stabilization of ultraviolet diode lasers by using dichroic atomic vapor spectroscopy and transfer cavity Danna Shen, ..., Xiang Zhang (2020)

Ultraviolet (UV) diode lasers are widely used in many photonics applications. But their frequency stabilization schemes are not as mature as frequency-doubling lasers, mainly due to some limitations in the UV spectral region. Here we developed a high-performance UV frequency stabilization technique implemented directly on UV diode lasers by combining the dichroic atomic vapor laser lock and the resonant transfer cavity lock. As an example, we demonstrate a stable locking with frequency standard deviations of approximately 200 KHz and 300 KHz for 399nm and 370nm diode lasers in 20 minutes. We achieve a long-term frequency drift of no more than 1 MHz for the target 370nm laser within an hour, which was further verified with fluorescence counts rates of a single trapped $^{171}$Yb$^+$ ion. We also find strong linear correlations between lock points and environmental factors such as temperature and atmospheric pressure.

While the paper discusses a technique for frequency stabilization of UV diode lasers, specifically about dichroic atomic vapor laser lock, it does not focus on modulation transfer spectroscopy. The error signal generation through modulation and demodulation is mentioned, but the specifics about its production and details about the electronic circuits are limited. There is also no specific mention of atomic vapor, which was an important aspect of the research query.

 🔴 [75]
Laser stabilization to an atomic transition using an optically generated dispersive lineshape Fabiano Queiroga, ..., Martine Chevrollier (2012)

We report on a simple and robust technique to generate a dispersive signal which serves as an error signal to electronically stabilize a monomode cw laser emitting around an atomic resonance. We explore nonlinear effects in the laser beam propagation through a resonant vapor by way of spatial filtering. The performance of this technique is validated by locking semiconductor lasers to the cesium and rubidiumD2 line and observing long-term reduction of the emission frequency drifts, making the laser well adapted for many atomic physics applications.

The paper in question discusses laser stabilization around an atomic resonance and does go into detail about the construction of the error signal and the electronic feedback circuits used to correct for frequency drift. However, this paper achieves laser locking by exploiting nonlinear effects in the propagation of the laser beam through resonant vapor, rather than through modulation transfer spectroscopy. The method described is distinct from modulation transfer spectroscopy and doesn't involve the use of a pump and probe beam, spectral broadening through frequency modulation, or phase-sensitive detection with a lock-in amplifier. Therefore, while it is tangentially related in that it also concerns laser locking to atomic transitions, the technique proposed is distinctly different from the modulation transfer spectroscopy, the specific topic of interest.

 🔴 [76]
Laser-cooled ytterbium ion frequency standard S. Mulholland, ..., P. Gill (2018)

We report on the development of a trapped-ion, microwave frequency standard based on the 12.6 GHz hyperfine transition in laser-cooled ytterbium-171 ions. The entire system fits into a 6U 19-inch rack unit ($51\times49\times28$ cm) and comprises laser, electronics, and physics package subsystems. The performance of this development system is evaluated; the fractional frequency instability was measured to be $3.6\times10^{-12}/\surd\tau$ for averaging times between 30 s and 1500 s.

The paper is about laser-cooled ytterbium ion frequency standard where atomic transitions have been studied, but there is no direct mention of modulation transfer spectroscopy or its implementation in laser locking. The paper discusses the laser stabilization process and the details of the electronic setup, factors that are relevant to the researcher's interest, but not the main focus. Given that the primary methodology that the researcher is interested in (MTS) isn't mentioned or explained in the paper, it's safe to say that it's not the central theme.

 🔴 [77]
Observation of optical Rabi oscillations in transmission signal of atomic vapor under continuous-wave laser excitation Aram Papoyan, ..., Svetlana Shmavonyan (2020)

We have studied the temporal behavior of the atomic absorption signal under resonant excitation with a continuous-wave laser radiation. Measurements done for D2 line of 85Rb with ~ 1 ns temporal resolution have shown irregular oscillatory behavior of the transmission signal, which becomes well pronounced for high laser power, and disappears when the laser is tuned off-resonance. Application of the fast Fourier transform analysis of the transmission signal reveals power-dependent frequency peaks, which are shown to be associated with Rabi frequency. Possible linkage of the observed results with the phase-to-amplitude noise conversion caused by the the phase fluctuations of laser field is discussed.

While this paper deals with an experiment conducted on atomic vapor (85Rb D2 line) using a continuous-wave laser, it does not focus on modulation transfer spectroscopy or its specific implementation in laser locking. The methodology involves frequency locking via a feedback loop, which is common in modulation transfer spectroscopy, but the actual techniques and equipment in the paper – e.g., a dichroic atomic vapor laser lock – are not in line with traditional modulation transfer spectroscopy setups. Also, the specifics about error signal generation and electronic circuits utilized, which are of particular interest to your research, are not comprehensively discussed.

 🔴 [78]
Isotope Shift Measurements of Stable and Short-Lived Lithium Isotopes for Nuclear Charge Radii Determination W. Nörtershäuser, ..., C. Zimmermann (2010)

Changes in the mean-square nuclear charge radii along the lithium isotopic chain were determined using a combination of precise isotope shift measurements and theoretical atomic structure calculations. Nuclear charge radii of light elements are of high interest due to the appearance of the nuclear halo phenomenon in this region of the nuclear chart. During the past years we have developed a new laser spectroscopic approach to determine the charge radii of lithium isotopes which combines high sensitivity, speed, and accuracy to measure the extremely small field shift of an 8 ms lifetime isotope with production rates on the order of only 10,000 atoms/s. The method was applied to all bound isotopes of lithium including the two-neutron halo isotope Li-11 at the on-line isotope separators at GSI, Darmstadt, Germany and at TRIUMF, Vancouver, Canada. We describe the laser spectroscopic method in detail, present updated and improved values from theory and experiment, and discuss the results.

This paper discusses a laser spectroscopic method applied to measure isotope shifts in lithium isotopes. Although it presents a detailed method of laser frequency stabilization, it does not directly address modulation transfer spectroscopy (MTS). Despite having details on the generation of error signals and the utilization of electronic circuits, the paper's focus deviates from the use of MTS in laser frequency locking. Therefore, while the paper provides useful context and detailed procedures in laser-based experimentations, it misses on directly addressing the key concept - MTS's implementation in laser locking.

 🔴 [79]
Velocity selective bi-polarization spectroscopy for laser cooling of metastable Krypton atoms Y. B. Kale, ..., H. S. Rawat (2014)

We report a velocity selective bi-polarization spectroscopy (VS-BPS) technique to generate a background-free, dispersion-like reference signal which is tunable over a wide range of frequency. In this technique, a pair of linearly polarized weak probe beams passing through a gas cell of metastable Krypton (Kr*) atoms, overlaps with a pair of counter-propagating circularly polarized strong pump beams derived from an independently tunable control laser. The polarization spectroscopy signals from the two probe beams, after subtraction, result in VS-BPS signal. The spectral shifting in VS-BPS signal can be achieved by tuning the frequency of the control laser. The dependence of the amplitude and slope of the VS-BPS signal on the RF power used for excitation of Kr atoms in the gas cell and on the power of pump beams has been studied. The frequency stability of a diode laser locked with VS-BPS signal has been found to be better than the frequency stability of the laser locked with a saturated absorption spectroscopy (SAS) signal. The VS-BPS signal is finally used for stabilization and tuning of the cooling laser frequency for a magneto-optical trap (MOT) for Kr* atoms.

While the paper discusses laser frequency locking, it specifically describes a technique called velocity selective bi-polarization spectroscopy (VS-BPS), not modulation transfer spectroscopy (MTS). The paper's focus is on generating a reference signal for frequency lock-point tuning in external cavity diode lasers. The details about error signal generation and associated circuitry are not explored. Though related to the broader topic of laser locking techniques, the paper does not contribute specifically to MTS and its implementation in laser locking. Further, the experiment conducted appeared to involve metastable Krypton atoms instead of atomic vapor.

 🔴 [80]
Measurement of the scalar polarizability of the indium $6p_{1/2}$ state using two-step atomic-beam spectroscopy Benjamin L. Augenbraun, ..., P. K. Majumder (2016)

We have completed a measurement of the Stark shift within the $^{115}$In $6s_{1/2} \rightarrow 6p_{1/2}$ excited-state transition using two-step laser spectroscopy in an indium atomic beam. Combining this measurement with recent experimental results we determine the scalar polarizability, $\alpha_{0}$, of the $6p_{1/2}$ state to be $7683 \pm43 \,a_{0}^{3}$ in atomic units, a result which agrees very well with recent theoretical calculations. In this experiment, one laser, stabilized to the $5p_{1/2} \rightarrow 6s_{1/2}$ 410~nm transition, was directed transversely to the atomic beam, while a second, overlapping laser was scanned across the 1343~nm $6s_{1/2} \rightarrow 6p_{1/2}$ transition. We utilized two-tone frequency-modulation spectroscopy of the infrared laser beam to measure the second-step absorption in the interaction region, where the optical depth is less than 10$^{-3}$. In the course of our experimental work we also determined the hyperfine splitting within the $6p_{1/2}$ state, improving upon the precision of an existing measurement.

The paper discusses frequency modulation spectroscopy for the stabilization of lasers, but does not specifically mention modulation transfer spectroscopy. It does provide details on the creation of an error signal for laser stabilization using frequency modulation spectroscopy, which is relevant to the topic. However, it does not provide a specific implementation of modulation transfer spectroscopy.

 🔴 [81]
Isotope Shifts in the 7s$\rightarrow$8s Transition of Francium: Measurements and Comparison to \textit{ab initio} Theory M. R. Kalita, ..., V. V. Flambaum (2017)

We observe the electric-dipole forbidden $7s\rightarrow8s$ transition in the francium isotopes $^{208-211}$Fr and $^{213}$Fr using a two-photon excitation scheme. We collect the atoms online from an accelerator and confine them in a magneto optical trap for the measurements. In combination with previous measurements of the $7s\rightarrow7p_{1/2}$ transition we perform a King Plot analysis. We compare the thus determined ratio of the field shift constants (1.230 $\pm$ 0.019) to results obtained from new ab initio calculations (1.234 $\pm$ 0.010) and find excellent agreement.

This scientific paper is centered around a two-photon excitation scheme in francium isotopes, and while it does discuss locking the frequencies of lasers, it doesn't specifically mention or delve into modulation transfer spectroscopy or its application in laser locking. Details on the generation of the error signal or electronic circuits used in the process are also not explicitly mentioned or discussed.

 🔴 [82]
The optical calcium frequency standards of PTB and NIST U. Sterr, ..., L. Hollberg (2004)

We describe the current status of the Ca optical frequency standards with laser-cooled neutral atoms realized in two different laboratories for the purpose of developing a possible future optical atomic clock. Frequency measurements performed at the Physikalisch-Technische Bundesanstalt (PTB) and the National Institute of Standards and Technology (NIST) make the frequency of the clock transition of 40Ca one of the best known optical frequencies (relative uncertainty 1.2e-14) and the measurements of this frequency in both laboratories agree to well within their respective uncertainties. Prospects for improvement by orders of magnitude in the relative uncertainty of the standard look feasible.

This paper primarily deals with optical frequency standards and the workings of optical atomic clocks, focusing on the techniques applied at NIST and PTB. It touches on the subject of laser spectroscopy and involves detailed description of the experimental setup. However, there is no explicit mention or detailed exploration of modulation transfer spectroscopy or laser locking. Moreover, no specific detail is provided related to the generation of the error signal and its implementation using electronic circuits. While the paper discusses experiments with laser-cooled atoms, the lack of explicit focus on modulation transfer spectroscopy and laser locking makes it less directly relevant to the specific topic of interest.

 🔴 [83]
Hyperfine spectroscopy using co-propagating pump-probe beams Alok K. Singh, ..., Vasant Natarajan (2010)

We have shown earlier that hyperfine spectroscopy in a vapor cell using co-propagating pump-probe beams has many advantages over the usual technique of saturated-absorption spectroscopy using counter-propagating beams. The main advantages are the absence of crossover resonances, the appearance of the signal on a flat (Doppler-free) background, and the higher signal-to-noise ratio of the primary peaks. Interaction with non-zero-velocity atoms causes additional peaks, but only one of them appears within the primary spectrum. We first illustrate the advantages of this technique for high-resolution spectroscopy by studying the $D_2$ line of Rb. We then use an acousto-optic modulator (AOM) for frequency calibration to make precise hyperfine-interval measurements in the first excited $P_{3/2}$ state of $^{85,87}$Rb and $^{133}$Cs.

This paper describes a technique of hyperfine spectroscopy using co-propagating pump-probe beams. While the technique shares similarities with modulation transfer spectroscopy, it is not exactly the same. The authors also mention applications such as laser locking, but don't directly discuss the error signal's generation or the specific electronic circuits. The study instead focuses on overcoming the problems associated with saturated-absorption spectroscopy and presenting a novel approach to hyperfine spectroscopy.

 🔴 [84]
Saturated-absorption spectroscopy: Eliminating crossover resonances using co-propagating beams Ayan Banerjee, ..., Vasant Natarajan (2003)

We demonstrate a new technique for saturated-absorption spectroscopy using co-propagating beams that does not have the problem of crossover resonances. The pump beam is locked to a transition and its absorption signal is monitored while the probe beam is scanned. As the probe comes into resonance with another transition, the pump absorption is reduced and the signal shows a Doppler-free dip. We use this technique to measure hyperfine intervals in the $D_2$ line of $^{85}$Rb with a precision of 70 kHz, and to resolve hyperfine levels in the $D_2$ line of $^{39}$K that are less than 10 MHz apart.

Based on the abstract and selected excerpts, this paper extensively discusses a new technique for saturated-absorption spectroscopy using co-propagating beams and how to eliminate crossover resonances. The problem of laser lock point shift is also addressed. While the paper details experimentation with atomic vapor (specifically using the D2 line of Rubidium and Potassium), it doesn't delve into the modulation transfer spectroscopy method for laser locking, which is the main focus of our research. This paper gives considerable focus to overlapping beam techniques and Doppler-free spectroscopy, but it lacks explicit discussion on generation of error signals and electronic circuits.

 🔴 [85]
Doppler-free saturation of the cascade fluorescence that follows excitation of the $5s \to 6p $ transition in atomic rubidium J. E. Navarro-Navarrete, ..., J. Jiménez-Mier (2019)

We present an experimental scheme that produces Doppler-free spectra of the $5s \to 6p $ second resonance transition in atomic rubidium. The experiment uses the saturation of the cascade fluorescence that occurs when thermal rubidium atoms interact with two counterpropagating $420 $ nm laser beams of comparable intensity. Part of the excited atomic population goes through the $5p_{3/2}$ level which then decays by emission of $780$ nm photons. Narrow dips appear in this otherwise broad $780$ nm fluorescence, which allows resolution of the $6p_{3/2}$ hyperfine structure. A rate equation model is used to interpret the spectra. It is also shown that these narrow peaks can be used to lock the frequency of the $420 $ nm laser. Using a second beam modulated in frequency produces three sets of spectra with known frequency spacings that can be used to perform an all-optical measurement of the hyperfine splittings of the $6p_{3/2} $ manifold in rubidium.

The paper under review discusses an experimental scheme that uses Doppler-free spectra to measure the hyperfine structure of rubidium and to lock the frequency of the laser used in the experiment. It mentions fluorescence dips which can be used for frequency locking. However, it does not explicitly detail how the error signal is generated or discuss the electronic circuits involved in the process, key elements that were mentioned as part of the topic of interest. Further, the paper does not seem to be centered around the use of modulation transfer spectroscopy - even though this is a common technique in similar experiments, it's not explicitly addressed in the abstract or selected parts of the paper.

 🔴 [86]
A self-locking Rydberg atom electric field sensor C. T. Fancher, ..., B. L. Schmittberger Marlow (2022)

A crucial step towards enabling real-world applications for quantum sensing devices such as Rydberg atom electric field sensors is reducing their size, weight, power, and cost (SWaP-C) requirements without significantly reducing performance. Laser frequency stabilization is a key part of many quantum sensing devices and, when used for exciting non-ground state atomic transitions, is currently limited to techniques that require either large SWaP-C optical cavities and electronics or use significant optical power solely for frequency stabilization. Here we describe a laser frequency stabilization technique for exciting non-ground state atomic transitions that solves these challenges and requires only a small amount of additional electronics. We describe the operation, capabilities, and limitations of this frequency stabilization technique and quantitatively characterize measure its performance. We show experimentally that Rydberg electric field sensors using this technique are capable of data collection while sacrificing only 0.1% of available bandwidth for frequency stabilization of noise up to 900 Hz.

The paper is relevant to frequency stabilization and laser locking but it doesn't specifically mention the use of modulation transfer spectroscopy. Instead, it focuses on a self-locking technique for Rydberg atom electric field sensors. It discusses the creation of the error signal and also provides some details about the electronics circuit involved (such as use of a lock-in amplifier and servo). While these discussions are generally valuable for understanding laser frequency stabilization and the generation of error signals, it doesn't address the specific interest in modulation transfer spectroscopy's role in these processes.

 🔴 [87]
Doppler-free two-photon resonances for atom detection and sum frequency stabilization A. M. Akulshin, ..., A. I. Sidorov (2011)

We investigate the excitation of the 5D_{5/2} level in Rb atoms using counter-propagating laser beams, which are nearly resonant to the one-photon 5S_{1/2} - 5P_{3/2} and 5P_{3/2} - 5D_{5/2} transitions, ensuring that a sum of the optical frequencies corresponds to the 5S_{1/2} - 5D_{5/2} transition. The excitation produced by two-photon and step-wise processes is detected via spontaneously emitted fluorescence at 420 nm arising from the 6P_{3/2} - 5S_{1/2} transition. The dependences of blue fluorescence intensity on atomic density and laser detuning from the intermediate 5P_{3/2} level have been investigated. The sensitivity of the frequency detuned bi-chromatic scheme for atom detection has been estimated. A novel method for sum frequency stabilization of two free-running lasers has been suggested and implemented using two-photon Doppler-free fluorescence and polarization resonances.

The paper provides information about the use of counter-propagating lasers in the context of atomic spectroscopy, using Rb atoms. It elaborates on excitation procedures, frequency stabilization, and atomic density measures. It does mention the use of a PID servo system, which would be part of the electronic circuits of interest. However, it does not specifically discuss modulation transfer spectroscopy (MTS) or the creation of the error signal for laser stabilization using MTS. Instead, it focuses on two-photon Doppler-free fluorescence and polarization resonances. These are certainly related techniques, but they are not the same as, or a focus on, MTS in the defined context.

 🔴 [88]
Optical atomic clocks N. Poli, ..., G. M. Tino (2014)

In the last ten years extraordinary results in time and frequency metrology have been demonstrated. Frequency-stabilization techniques for continuous-wave lasers and femto-second optical frequency combs have enabled a rapid development of frequency standards based on optical transitions in ultra-cold neutral atoms and trapped ions. As a result, today's best performing atomic clocks tick at an optical rate and allow scientists to perform high-resolution measurements with a precision approaching a few parts in $10^{18}$. This paper reviews the history and the state of the art in optical-clock research and addresses the implementation of optical clocks in a possible future redefinition of the SI second as well as in tests of fundamental physics.

This paper discusses several frequency-stabilization techniques including modulation of light sent to a cavity. It does lack explicit mention of Modulation Transfer Spectroscopy (MTS). While the methods discussed for laser locking, error signal generation and feedback mechanisms are general to various frequency stabilization techniques like MTS, it does not focus explicitly on MTS or on atomic vapor. Many details about the electronic circuits used are also not specified. The paper is more focused on frequency standards based on optical transitions in ultra-cold neutral atoms and trapped ions as well as a history and future trends of optical-clock research.

 🔴 [89]
Observation of sub-natural linewidths for cold atoms in a magneto-optic trap Umakant D. Rapol, ..., Vasant Natarajan (2002)

We have studied the absorption of a weak probe beam through cold rubidium atoms in a magneto-optic trap. The absorption spectrum shows two peaks with the smaller peak having linewidth as small as 28% of the natural linewidth. The modification happens because the laser beams used for trapping also drive the atoms coherently between the ground and excited states. This creates ``dressed'' states whose energies are shifted depending on the strength of the drive. Linewidth narrowing occurs due to quantum coherence between the dressed states. The separation of the states increases with laser intensity and detuning, as expected from this model.

Although the paper focuses on precision spectroscopy in a magneto-optic trap, it does not directly address the use of modulation transfer spectroscopy for laser locking. The paper primarily discusses the observation of sub-natural linewidths in cold rubidium atoms and the role of 'dressed' states, which is a concept different from modulation transfer spectroscopy. Furthermore, the provided excerpts do not provide details on the generation of an error signal, which is crucial in modulation transfer spectroscopy and a key part of the topic specified. There is also no mention of the electronic circuits involved, another significant part of the request.

 🔴 [90]
Hyperfine structure of laser-cooling transitions in fermionic erbium-167 Albert Frisch, ..., Svetlana Kotochigova (2013)

We have measured and analyzed the hyperfine structure of two lines, one at 583nm and one at 401nm, of the only stable fermionic isotope of atomic erbium as well as determined its isotope shift relative to the four most-abundant bosonic isotopes. Our work focuses on the J->J+1 laser cooling transitions from the [Xe] 4f12 6s2 (3H6) ground state to two levels of the excited [Xe] 4f12 6s6p configuration, which are of major interest for experiments on quantum degenerate dipolar Fermi gases. From a fit to the observed spectra of the strong optical transition at 401nm we find that the magnetic dipole and electric quadrupole hyperfine constants for the excited state are Ae/h=-100.1(3)MHz and Be/h=-3079(30)MHz, respectively. The hyperfine spectrum of the narrow transition at 583nm, was previously observed and accurate Ae and Be coefficients are available. A simulated spectrum based on these coefficients agrees well with our measurements. We have also determined the hyperfine constants using relativistic configuration-interaction ab initio calculations. The agreement between the ab initio and fitted data for the ground state is better than 0.1%, while for the two excited states the agreement is 1% and 11% for the Ae and Be constants, respectively.

While the paper does discuss Doppler-free modulation transfer spectroscopy in the context of measuring the hyperfine structure and the isotope shift of erbium, the paper's main focus seems tilted toward the investigation of hyperfine constants and spectral features of erbium isotopes rather than actualizing the concept of laser locking. It provides important insights such as modulation methods and the extraction of spectroscopy signals, which are related to the error signal generation, but it does not appear to dive into details about laser locking itself or the specific electronic circuits used for the process.

 🔴 [91]
Metrological characterization of the pulsed Rb clock with optical detection Salvatore Micalizio, ..., Filippo Levi (2011)

We report on the implementation and the metrological characterization of a vapor-cell Rb frequency standard working in pulsed regime. The three main parts that compose the clock, physics package, optics and electronics, are described in detail in the paper. The prototype is designed and optimized to detect the clock transition in the optical domain. Specifically, the reference atomic transition, excited with a Ramsey scheme, is detected by observing the interference pattern on a laser absorption signal. \ The metrological analysis includes the observation and characterization of the clock signal and the measurement of frequency stability and drift. In terms of Allan deviation, the measured frequency stability results as low as $1.7\times 10^{-13} \ \tau^{-1/2}$, $\tau$ being the averaging time, and reaches the value of few units of $10^{-15}$ for $\tau=10^{4}$ s, an unprecedent achievement for a vapor cell clock. We discuss in the paper the physical effects leading to this result with particular care to laser and microwave noises transferred to the clock signal. The frequency drift, probably related to the temperature, stays below $10^{-14}$ per day, and no evidence of flicker floor is observed. \ We also mention some possible improvements that in principle would lead to a clock stability below the $10^{-13}$ level at 1 s and to a drift of few units of $10^{-15}$ per day.

The paper describes an experiment involving a gas cell Rb frequency standard working in a pulsed regime, with a focus on the physics package, optics, and electronics. The laser is frequency-stabilized using a third-harmonic frequency control loop. However, the paper does not make mention of Modulation Transfer Spectroscopy, nor focus on the specific process of laser locking through error signal generation. Although the paper discusses aspects like laser frequency stabilization, it doesn't address the specific method of Modulation Transfer Spectroscopy.

 🔴 [92]
An ultraviolet laser system for laser cooling and trapping of metastable magnesium A. P. Kulosa, ..., E. M. Rasel (2012)

We report on a reliable laser system for cooling magnesium atoms in the metastable 3P manifold. The three relevant transitions coupling the 3P to the 3D manifold are near 383 nm and seperated by several hundred GHz. The laser system consists of three diode lasers at 766 nm. All lasers are frequency stabilised to a single pre-stabilised transfer cavity. The applied scheme for frequency control greatly reduces the complexity of operating three lasers combined with resonant frequency doubling stages and provides a high reliability necessary for complex atomic physics experiments.

The paper discusses the construction of a laser system for cooling magnesium atoms, and although it does make mention of the use of diode lasers locked to a transfer cavity via the Pound-Drever-Hall (PDH) method, does not specifically reference modulation transfer spectroscopy. The creation of the error signal, its role, and details about the electronic circuits involved in the system are discussed partially. However, the use of MTS isn't explicitly made clear in the description.

 🔴 [93]
Controlled insertion and retrieval of atoms coupled to a high-finesse optical resonator Mkrtych Khudaverdyan, ..., Dieter Meschede (2008)

We experimentally investigate the interaction between one and two atoms and the field of a high-finesse optical resonator. Laser-cooled caesium atoms are transported into the cavity using an optical dipole trap. We monitor the interaction dynamics of a single atom strongly coupled to the resonator mode for several hundred milliseconds by observing the cavity transmission. Moreover, we investigate the position-dependent coupling of one and two atoms by shuttling them through the cavity mode. We demonstrate an alternative method, which suppresses heating effects, to analyze the atom-field interaction by retrieving the atom from the cavity and by measuring its final state.

The provided paper investigates the interaction between atoms and the field of a high-finesse optical resonator. It discusses laser locking schemes and provides detailed descriptions of the error signal and electronic circuitry involved. However, the paper does not seem to discuss or involve modulation transfer spectroscopy specifically in their locking scheme. Instead, they rely on the Pound-Drever-Hall method for generating error signals. Therefore, while the paper does discuss laser locking and gives detailed accounts of the associated electronic systems, it fails to directly address the specific topic of modulation transfer spectroscopy's application in this context.

 🔴 [94]
Coherent laser spectroscopy of highly charged ions using quantum logic P. Micke, ..., P. O. Schmidt (2020)

Precision spectroscopy of atomic systems is an invaluable tool for the advancement of our understanding of fundamental interactions and symmetries. Recently, highly charged ions (HCI) have been proposed for sensitive tests of physics beyond the Standard Model and as candidates for high-accuracy atomic clocks. However, the implementation of these ideas has been hindered by the parts-per-million level spectroscopic accuracies achieved to date. Here, we cool a trapped HCI to the lowest reported temperatures, and introduce coherent laser spectroscopy on HCI with an eight orders of magnitude leap in precision. We probe the forbidden optical transition in $^{40}$Ar$^{13+}$ at 441 nm using quantum-logic spectroscopy and measure both its excited-state lifetime and $g$-factor. Our work ultimately unlocks the potential of HCI, a large, ubiquitous atomic class, for quantum information processing, novel frequency standards, and highly sensitive tests of fundamental physics, such as searching for dark matter candidates or violations of fundamental symmetries.

While this paper does discuss the stabilization of lasers at a high degree of precision, it makes no mention of modulation transfer spectroscopy, a key component of the desired topic. Instead, the researchers use quantum-logic spectroscopy for precision measurements. The error signal generation and the relevant electronic circuits are indeed detailed, but without the context of MTS, these details may not be directly relevant to the desired topic.

 🔴 [95]
Laser Phase and Frequency Stabilization Using Atomic Coherence Yoshio Torii, ..., Takatoshi Aoki (2012)

We present a novel and simple method of stabilizing the laser phase and frequency by polarization spectroscopy of an atomic vapor. In analogy to the Pound-Drever-Hall method, which uses a cavity as a memory of the laser phase, this method uses atomic coherence (dipole oscillations) as a phase memory of the transmitting laser field. A preliminary experiment using a distributed feedback laser diode and a rubidium vapor cell demonstrates a shot-noise-limited laser linewidth reduction (from 2 MHz to 20 kHz). This method would improve the performance of gas-cell-based optical atomic clocks and magnetometers and facilitate laser-cooling experiments using narrow transitions.

The paper provides a detailed explanation of a method for stabilizing laser phase and frequency using polarization spectroscopy on atomic vapor - specifically mentioning rubidium. However, while the technique shares similarities with Modulation Transfer Spectroscopy, it doesn't explicitly mention or focus on Modulation Transfer Spectroscopy. The paper does discuss error signal generation and the electronic circuits, but the method employed varies a bit from the topic of interest. Hence, while the paper is topically relevant, it diverges in its choice of spectroscopy method.