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Abstract
Compactness, robustness and autonomy of optical frequency references are prerequisites for reliable operation in mobile systems, on ground as well as in space. We present a standalone plug and play optical frequency reference device based on frequency modulation spectroscopy of the D2-transition in rubidium at 780 nm. After a single button press the hand-sized laser module, based on the micro-integrated laser-optical bench described in [J. Opt. Soc. Am. B 38, 1885 (2021) [CrossRef] ], works fully autonomous and generates 6 mW of frequency stabilized light with a relative frequency instability of 1.4×10−12 at 1 s and below 10−11 at 105 s averaging time. We describe the design of the device, investigate the thermal characteristics affecting the output frequency and demonstrate short-term frequency stability improvement by a Bayesian optimizer varying the modulation parameters.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Atomic optical frequency references (AOFR) are critical subsystems of cold-atom based quantum sensors and optical clocks. These technologies can contribute to fundamental science [1,2], ground- and space-based earth observation [3,4] and navigation [5,6]. Other use cases for AOFRs are for example the calibration of optical instruments, e.g. wavelength meters [7,8], or absolute referencing of laser systems for trace-gas detection [9] or optical communication [10].
Ideally, AOFRs serve as robust and reliable sources of frequency-stabilized laser light without further interaction with the hosting system. Functional and physical isolation is therefore advantageous allowing for improved predictability of the performance after integration. They are thus particularly well suited for realizations as standalone modules. However, the technological challenges of AOFR development are diverse, comprising the mechanical and thermal design, the integration of a reliable laser light source, the optical engineering of a spectroscopy unit and the development of suitable low-noise driving electronics. This motivates segmentation. For instance, sounding rocket missions demonstrated AOFRs in space realized by separate laser, optics and electronics subsystems [11–13] instead of one integrated module each. This design philosophy is reinforced when multiple lasers and electronics control units are required, which is the case for complex cold-atom applications [14,15]. To allow for a transition from mission dedicated system development to flexible commercial realizations of cold-atom quantum sensors, optical clocks, wavelength meters or other laser systems, compact stand-alone AOFR modules are necessary.
The most advanced AOFR modules belong to the domain of warm atomic vapors. Optical clocks utilizing coherent population trapping [16], such as the chip scale atomic clocks [17,18], are available as commercial-off-the-shelf (COTS) components [19]. Developed as integrated clocks, they generate a 10 MHz output signal and thus can’t be used directly for optical referencing of cold-atom quantum sensors or optical instruments.
Turn-key solutions with optical output do exist. However, to our knowledge they are either only available at telecommunication wavelengths and achieve relative frequency instabilities at the 10$^{-9}$ level at 1 s averaging time [20,21] or lack the compactness necessary for the aforementioned applications [22,23]. COTS frequency discriminator modules based on alkali-metals [24,25] can be used to achieve lower instabilities and research on a high-performing one based on modulation transfer spectroscopy (MTS) has been presented recently [26]. These require a suitable external laser input and electronics control unit. Commercial laser packages with integrated reference cells [27] leave only the development of additional electronics and software open to the user.
We present a standalone, hand-sized plug and play AOFR system based on the laser module we presented in [28] with a distributed feedback (DFB) laser diode utilizing the D2-transition of warm rubidium vapor at 780 nm. The system achieves relative instabilities of 1.4$\times$10$^{-12}$ at 1 s and below 10$^{-11}$ up to 10$^5$ s averaging time. Powering it leads to autonomous thermal stabilization of the optical bench. A button press activates the laser and reliably initiates the frequency stabilization to a predefined atomic transition.
The work is structured as follows. Section 2 gives an overview over the system components and functions with a summary of the achieved size, weight and power (SWaP). In Section 3, the thermal characteristics such as warm-up time of the device and temperature sensitivity of the optical frequency are investigated. The utility of an automated Bayesian optimization process for the instability minimization is exemplarily demonstrated in Section 4. Section 5 discusses the achieved performance in terms of the Allan deviation. Finally, in Section 6, the results are summarized and an outlook for future developments and potential use-cases of the device is given.
2. System overview
The frequency reference system is built around the optical module presented in [28]. There, a DFB laser diode is integrated with a rubidium vapor cell and a detector into a single, temperature stabilized module for frequency modulation spectroscopy of the D2-line at 780 nm. To realize a stand-alone system, a dedicated software and the following additional subsystems embedded in a housing are needed: a control and lock-in amplification unit, a temperature controller and a current driver. In the presented module, this is addressed by utilizing the RedPitaya StemLab 125-14 (RP) and a custom extension board, which hosts a commercial temperature controller (Meerstetter TEC-1092) attached to the bottom side as well as an integrated current driver developed in our group based on a modified Libbrecht-Hall design [29]. A system overview is given in Fig. 1.
Fig. 1. System Overview. (a) Simplified functional scheme excluding the monitoring functions for temperature controller status and laser diode current. (b) Explosion including the optical module, the RedPitaya StemLab, a compact temperature controller and the driver extension board for signal distribution and current driving. (c) Assembled system without cover with dimensions annotated. (d) Complete system with cover. Image Credits (c,d): P. Immerz (FBH).
To accommodate a compact design, the standard heat-sink of the RP is replaced by a flat piece of aluminum and unused connectors are removed. A thermal pad between the RP and the structured base plate ensures sufficient cooling. The system can be mounted on rubber stands and is still capable to operate with passive air cooling at room temperature. To monitor the device temperature, a thermistor is installed on the base plate next to the optical module. The connection to the optical module is realized by MCX-plugs soldered to the extension board.
A software developed on the basis of Linien [30,31] runs on the RP and fulfills the following tasks: monitoring of the temperature controller status, control of the current set-point, monitoring of the driving current and the device temperature, generation of the current sweep and modulation signal, demodulation of the spectroscopy signal, frequency locking with a bandwidth of 700 kHz and, finally, control of the front-panel LEDs. The RGB-LED integrated in the button indicates the general device status (idle, running, error). The remaining three red LEDs indicate the status of the temperature (stable/ramping), the current (on/off) and the frequency lock (locked/unlocked), respectively. A rubber cylinder is used as the feedthrough and strain relief of the polarization maintaining optical fiber. The rear panel gives access to the standard interface of the RP, comprising connectors for the power supply (micro-USB), USB type A and Ethernet.
Table 1 summarizes the system’s SWaP as it is depicted in Figure 1. The optical output power from the polarization maintaining fiber is 6 mW.
Table 1. Size, weight and power consumption of the frequency reference as depicted in Fig. 1 d).
While the device works completely autonomous after the button on the front-panel is pressed, it can be connected to a network to monitor and control system parameters as well as for the selection of the transition to be locked on.
3. Thermal characteristics
The system is passively cooled by its casing. With a constant ambient temperature, the device temperature during the warm-up process $T(t)$ can be modelled by Newton’s law of cooling [32]:
where $\Delta T(t)$ is defined as $\Delta T(t)=T(t)-T(0)$, $A=T_{\mathrm {final}}-T(0)$ is the maximum temperature change and $\tau$ is a time constant defined by the heat capacitance and thermal conductance. To characterize the warm-up process in regard to its effect on the optical frequency, the latter is measured as soon as the laser is locked, which happens approximately 2 minutes after the cold start. In case of a warmed-up system, ramping up the laser current, stabilizing the laser diode temperature to 37 $^{\circ }$C and initializing the lock does only take 20 s. Currently, this time is limited by the manually defined minimum settling time for the temperature (10 s) and can be optimized if needed. A beat-note measurement with a second rubidium-based Ref. [33] utilizing MTS serves for measuring the frequency change. Figure 2 shows the measurement setup. In Fig. 3(a) we analyze the absolute frequency change over time with Eq. (1). Two scenarios are shown: the blue line shows a measurement where the system is isolated from the optical table by the rubber stands. The green line shows the measurement with the reference being in contact with the optical table. Both measurements happened at an ambient temperature of 20 $^{\circ }$C. In the first case, the device temperature approaches 39 $^{\circ }$C and the optical frequency settles after about 50 minutes. Under these conditions the Xilinx field-programmable gate-array of the RP reports an internal temperature of 48 $^{\circ }$C, which is well below the recommended maximum operating temperature of 85 $^{\circ }$C [34]. With the stands removed, the temperature settles at 28 $^{\circ }$C after about 12 minutes. Since the changes in optical frequency in both cases are in the range of tens of kHz, the AOFR can be used for rubidium cold atom applications 2 minutes after cold start and immediately after locking from stand-by mode.Fig. 3. Warm-up process of the system. (a) A frequency deviation of 4 kHz, corresponding to a relative deviation of 10$^{-11}$, from the final frequency value is reached after about 3000 s, when the system is mounted on rubber stands (blue). When in direct contact with the optical table (green), this level is reached after about 700 s. (b) Temperature dependence of the beat-note frequency. The measured frequencies are adjusted to match at 28 $^{\circ }$C. The dependence of 2.6 kHz K$^{-1}$ corresponds to a relative frequency deviation of 6.8$\times$10$^{-12}$ K$^{-1}$.
Figure 3(b) shows a linear relationship between the device temperature and the optical frequency of 2.6 kHz K$^{-1}$. At an optical frequency of 384 THz, this corresponds to a relative frequency deviation of 6.8$\times$10$^{-12}$ K$^{-1}$. Thus, we can approximate that frequency instabilities below 10$^{-12}$ require a temperature instability lower than 150 mK. The following measurements were executed with the rubber stands removed.
Figure 4 shows the results of a long-term frequency stability measurement, where the laboratory temperature changed by more than 0.5 K over the course of 15 h. The frequency response in c) is stronger by a factor of 10 than expected from the measured device temperature. This might indicate that the second reference laser, which is placed in the same laboratory, has led to a higher temperature sensitivity and the measured long-term stability needs to be considered an upper limit.
Fig. 4. Measurement of the impact of temperature changes in the laboratory. After 2 h the temperature rises from 19.7 $^{\circ }$C to 20 $^{\circ }$C and sinks down to 19.5 $^{\circ }$C after 6 h. A clear correlation between the laboratory temperature (a), the device temperature (b) and the beat-note frequency (c) can be identified. The predicted beat-note frequency (orange) is calculated using the temperature coefficient from Fig. 3 based on the device temperature. The frequency variations are too small by a factor of 10 in comparison to the measured ones (blue). This observation is suspected to be attributable to the second reference laser.
4. Optimization of the Allan deviation
Initial optimization of the signal-to-noise ratio by increasing the modulation amplitude lead to the expected improvement of the short-term stability below 100 ms averaging time. However, at longer averaging times, a deterioration from the $\tau ^{-{1/2}}$ trend correlating with the modulation amplitude was observed. The Allan deviation for averaging times between 100 ms and 10 s is thus optimized with a Bayesian optimizer contained in the software package JCMsuite [35] tuning the PID parameters of the lock and the modulation amplitude. The fitness function is chosen as:
In the case of $\sigma _y(\tau )=a\frac {10^{-12}}{\sqrt {\tau }}$, $a$ is then given by $10^{F/2}$.
The beat-note frequency is recorded every 100 ms for 600 s in total, to reduce the statistical error up to 10 s averaging time. Figure 5(a) shows the fitness and corresponding parameters sorted for descending fitness. The parameters were limited by the values indicated by the y-axis tick labels to avoid losing the lock during the optimization. The transfer functions corresponding to the unitless PID values can be found in [30]. The modulation amplitude converges to a value of 0.52$\pm$0.04 V and the proportional parameter of the PID tends to 3700$\pm$800 towards the lowest fitness values. The two other parameters have no observable effect on the overall fitness. The initial parameters were set to Vmod=0.95 V and P=5000. The optimized Allan deviation is reduced at times longer than 130 ms on the cost of an increase at lower averaging times. This can be explained by a reduced signal-to-noise ratio due to a lower signal amplitude with lower modulation amplitude. The fitness is reduced from 0.73 to 0.28. The reason for the deterioration with increasing modulation amplitude is subject of ongoing investigations and might be the result of the side-band amplitude affecting the measurement with the frequency-counter [36].
Fig. 5. Results of an exemplary Bayesian optimization process following initial manual optimization. (a) The steps are sorted based on descending fitness to visualize the convergence of the parameters. The strongest dependence is found on the modulation amplitude (b), while the PID parameters (c-e) show weak to no convergence. (f) Comparison of Allan deviation before and after the optimization process. The stability at 1 s averaging time was improved by a factor of 2. (g) The fitness is illustrated by the shaded area below the two graphs. Deviations from a horizontal line indicate deviations from the $\tau ^{-{1/2}}$ trend.
5. Performance
Figure 6 shows the frequency stability for averaging times from 10$^{-3}$ s to 10$^{5}$ s. The displayed Allan deviation is composed of three measurement series with different measurement times and sampling rates: 10 s with 1 kHz, 10$^{3}$ s with 10 Hz, and finally 2$\times$10$^{5}$ s with 0.1 Hz. For comparison, the Allan deviation from [28], where the optical module was driven with external laboratory drivers, is shown. As a result of the optimization process described in Section 4 the Allan deviation is reduced to 1.4$\times$10$^{-12}$ at 1 s averaging time. Despite the integration of all functional subsystems into a hand-held device, we managed to keep the increase of the frequency instability below 15 % up to 100 s averaging time. The increase of the long-term instability to a value of 7$\times$10$^{-12}$ at an averaging time of 10$^{5}$ s is suspected to be due to a less stable laboratory temperature during the new measurement.
Fig. 6. Comparison of the Allan deviation of the optical system driven by external laboratory drivers [28] and the fully integrated system. An increased deviation at long time scales might be the result of stronger temperature fluctuations in the laboratory.
6. Discussion
We have presented a fully-autonomous integrated AOFR enabling user-friendly access to frequency stabilized light at 780 nm with a relative frequency instability of 1.4$\times$10$^{-12}$ at 1 s and below 10$^{-11}$ at 10$^5$ s averaging time. A combination of adapted COTS components and custom electronics allowed for a compact, yet cost-efficient design. We have shown that under standard laboratory conditions the system is locked with initial relative frequency deviations of 2.6$\times$10$^{-11}$ after 2 minutes following a cold start. After a warm-up period of 12 minutes a minimum Allan deviation of 4$\times$10$^{-13}$ at 100 seconds averaging time is achieved. We could also demonstrate an exemplary application of a Bayesian optimizer to short-term frequency instabilities, where we achieved a reduction by up to a factor of 2.
Both, power consumption and warm-up time can be expected to be further reduced by a custom control unit instead of the RP. The temperature sensitivity of 6.8$\times$10$^{-12}$ K$^{-1}$ is likely to limit the long-term stability in most applications if not compensated for by an additional temperature stabilization of the casing. Under temporarily stable laboratory temperatures we observed a flicker noise floor at about 4$\times$10$^{-13}$ from 50 s to 400 s averaging time, while temperature variations predicted a variation of 2$\times$10$^{-13}$. Considering the small difference, temperature variations could also be limiting at medium timescales and an optimized thermal design might enable reaching a lower noise floor. The device in its current state may be used for cold-atom experiments in laboratories or as a building block for future cold-atom quantum sensors and wavelength measurements or calibration.
Our platform can be adapted for referencing to other alkali-vapors like potassium [11] or cesium [37], but also for more advanced schemes. To achieve long-term stabilities relevant to optical clock applications for navigation, compact AOFRs based on the two-photon transition at 778 nm are promising candidates [38,39]. Here, using MEMS vapor cells instead of glass-blown ones could improve the scalability of the device. Further size reduction is achieved by photonic integration of such vapor cells [40]. Intrinsically higher short-term stability compared to the presented D2-line based system could also be realized utilizing a GaN laser diode and the 5S-6P transition at 420nm in rubidium [41].
Funding
Bundesministerium für Wirtschaft und Energie (50RK1971, 50WM2066); Berlin University Alliance.
Acknowledgments
The authors greatly thank the workshop at Humboldt-Universität zu Berlin for technical support and B. Leykauf for providing the second reference for the beat-note measurements.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
References
1. M. S. Safronova, D. Budker, D. DeMille, D. F. J. Kimball, A. Derevianko, and C. W. Clark, “Search for new physics with atoms and molecules,” Rev. Mod. Phys. 90(2), 025008 (2018). [CrossRef]
2. B. Altschul, Q. G. Bailey, L. Blanchet, K. Bongs, P. Bouyer, L. Cacciapuoti, S. Capozziello, N. Gaaloul, D. Giulini, J. Hartwig, L. Iess, P. Jetzer, A. Landragin, E. Rasel, S. Reynaud, S. Schiller, C. Schubert, F. Sorrentino, U. Sterr, J. D. Tasson, G. M. Tino, P. Tuckey, and P. Wolf, “Quantum tests of the einstein equivalence principle with the ste–quest space mission,” Adv. Space Res. 55(1), 501–524 (2015). [CrossRef]
3. X. Wu, Z. Pagel, B. S. Malek, T. H. Nguyen, F. Zi, D. S. Scheirer, and H. Müller, “Gravity surveys using a mobile atom interferometer,” Sci. Adv. 5(9), 1 (2019). [CrossRef]
4. K. Bongs, M. Holynski, J. Vovrosh, P. Bouyer, G. Condon, E. Rasel, C. Schubert, W. P. Schleich, and A. Roura, “Taking atom interferometric quantum sensors from the laboratory to real-world applications,” Nat. Rev. Phys. 1(12), 731–739 (2019). [CrossRef]
5. T. Schuldt, M. Gohlke, M. Oswald, J. Wüst, T. Blomberg, K. Döringshoff, A. Bawamia, A. Wicht, M. Lezius, K. Voss, M. Krutzik, S. Herrmann, E. Kovalchuk, A. Peters, and C. Braxmaier, “Optical clock technologies for global navigation satellite systems,” GPS Solut. 25(3), 83 (2021). [CrossRef]
6. I. Georgescu, “A trapped ion atomic clock in space,” Nat. Rev. Phys. 3(7), 460 (2021). [CrossRef]
7. M. Verlinde, K. Dockx, S. Geldhof, K. König, D. Studer, T. E. Cocolios, R. P. de Groote, R. Ferrer, Y. Kudryavtsev, T. Kieck, I. Moore, W. Nörtershäuser, S. Raeder, P. V. den Bergh, P. V. Duppen, and K. Wendt, “On the performance of wavelength meters: Part 1—consequences for medium-to-high-resolution laser spectroscopy,” Appl. Phys. B 126(5), 85 (2020). [CrossRef]
8. K. König, P. Imgram, J. Krämer, B. Maaß, K. Mohr, T. Ratajczyk, F. Sommer, and W. Nörtershäuser, “On the performance of wavelength meters: Part 2—frequency-comb based characterization for more accurate absolute wavelength determinations,” Appl. Phys. B 126(5), 86 (2020). [CrossRef]
9. R. Matthey, W. Moreno, F. Gruet, P. Brochard, S. Schilt, and G. Mileti, “Rb-stabilized laser at 1572 nm for CO2 monitoring,” J. Phys.: Conf. Ser. 723, 012034 (2016). [CrossRef]
10. O. Terra and H. Hussein, “An ultra-stable optical frequency standard for telecommunication purposes based upon the 5s1/2 → 5d5/2 two-photon transition in rubidium,” Appl. Phys. B 122(2), 27 (2016). [CrossRef]
11. A. N. Dinkelaker, M. Schiemangk, V. Schkolnik, A. Kenyon, K. Lampmann, A. Wenzlawski, P. Windpassinger, O. Hellmig, T. Wendrich, E. M. Rasel, M. Giunta, C. Deutsch, C. Kürbis, R. Smol, A. Wicht, M. Krutzik, and A. Peters, “Autonomous frequency stabilization of two extended-cavity diode lasers at the potassium wavelength on a sounding rocket,” Appl. Opt. 56(5), 1388 (2017). [CrossRef]
12. M. Lezius, T. Wilken, C. Deutsch, M. Giunta, O. Mandel, A. Thaller, V. Schkolnik, M. Schiemangk, A. Dinkelaker, A. Kohfeldt, A. Wicht, M. Krutzik, A. Peters, O. Hellmig, H. Duncker, K. Sengstock, P. Windpassinger, K. Lampmann, T. Hülsing, T. W. Hänsch, and R. Holzwarth, “Space-borne frequency comb metrology,” Optica 3(12), 1381 (2016). [CrossRef]
13. K. Döringshoff, F. B. Gutsch, V. Schkolnik, C. Kürbis, M. Oswald, B. Pröbster, E. V. Kovalchuk, A. Bawamia, R. Smol, T. Schuldt, M. Lezius, R. Holzwarth, A. Wicht, C. Braxmaier, M. Krutzik, and A. Peters, “Iodine frequency reference on a sounding rocket,” Phys. Rev. Appl. 11(5), 054068 (2019). [CrossRef]
14. E. R. Elliott, M. C. Krutzik, J. R. Williams, R. J. Thompson, and D. C. Aveline, “NASA’s cold atom lab (CAL): system development and ground test status,” npj Microgravity 4(1), 16 (2018). [CrossRef]
15. K. Frye, S. Abend, W. Bartosch, A. Bawamia, D. Becker, H. Blume, C. Braxmaier, S.-W. Chiow, M. A. Efremov, W. Ertmer, P. Fierlinger, T. Franz, N. Gaaloul, J. Grosse, C. Grzeschik, O. Hellmig, V. A. Henderson, W. Herr, U. Israelsson, J. Kohel, M. Krutzik, C. Kürbis, C. Lämmerzahl, M. List, D. Lüdtke, N. Lundblad, J. P. Marburger, M. Meister, M. Mihm, H. Müller, H. Müntinga, A. M. Nepal, T. Oberschulte, A. Papakonstantinou, J. Perovsüek, A. Peters, A. Prat, E. M. Rasel, A. Roura, M. Sbroscia, W. P. Schleich, C. Schubert, S. T. Seidel, J. Sommer, C. Spindeldreier, D. Stamper-Kurn, B. K. Stuhl, M. Warner, T. Wendrich, A. Wenzlawski, A. Wicht, P. Windpassinger, N. Yu, and L. Wörner, “The bose-einstein condensate and cold atom laboratory,” EPJ Quantum Technol. 8(1), 1 (2021). [CrossRef]
16. B. D. Agap’ev, M. B. Gornyĭ, B. G. Matisov, and Y. V. Rozhdestvenskiĭ, “Coherent population trapping in quantum systems,” Phys.-Usp. 36(9), 763–793 (1993). [CrossRef]
17. S. Knappe, P. D. D. Schwindt, V. Shah, L. Hollberg, J. Kitching, L. Liew, and J. Moreland, “A chip-scale atomic clock based on 87rb with improved frequency stability,” Opt. Express 13(4), 1249 (2005). [CrossRef]
18. R. Lutwak, A. Rashed, M. Varghese, G. Tepolt, J. LeBlanc, M. Mescher, D. K. Serkland, K. M. Geib, G. M. Peake, and S. Römisch, “The chip-scale atomic clock - prototype evaluation,” in Proceedings of the 39th Annual Precise Time and Time Interval Meeting, (ION, 2007), pp. 269–290.
19. Microsemi, “Leading-edge technology enables a chip scale atomic clock,” https://www.microsemi.com/product-directory/clocks-frequency-references/3824-chip-scale-atomic-clock-csac (2021).
20. Thorlabs, Inc., “1.533 m Frequency-Locked Laser,” https://www.thorlabs.com/newgrouppage9.cfm?objectgroup_id=11688&pn=LLD1530 (2021).
21. Wavelength References, Inc., “Frequency Locked Lasers,” https://www.wavelengthreferences.com/product/frequency-locked-lasers/ (2021).
22. Winters Electro-Optics, Inc., “Model 200 Offset-Locked Iodine-Stabilized He-Ne Laser,” http://www.winterseo.com/m200.html (2021).
23. HighFinesse GmbH, “SLR 780,” https://www.highfinesse.com/en/calibrationsources/slr-780.html (2021).
24. TOPTICA Photonics AG, “Compact Saturation Spectroscopy,” https://www.toptica.com/products/optical-isolators-photonicals/photonicals/compact-saturation-spectroscopy/ (2021).
25. Vescent Photonics, LLC, “2-210 Saturated Absorption Spectroscopy Module,” https://vescent.com/de/d2-210-saturated-absorption-spectroscopy-module.html (2021).
26. S. Lee, S.-B. Lee, S. E. Park, H.-G. Hong, M.-S. Heo, S. Seo, J. Jeong, T. Y. Kwon, and G. Moon, “Compact modulation transfer spectroscopy module for highly stable laser frequency,” Opt. Lasers Eng. 146, 106698 (2021). [CrossRef]
27. W. Dorward, S. T. Lee, D. Bremner, S. Robertson, B. Jones, C. Carson, and L. McKnight, “The application of telecoms-style packaging techniques to narrow linewidth laser modules for quantum technologies,” in Components and Packaging for Laser Systems V, A. L. Glebov and P. O. Leisher, eds. (SPIE, 2019).
28. A. Strangfeld, S. Kanthak, M. Schiemangk, B. Wiegand, A. Wicht, A. Ling, and M. Krutzik, “Prototype of a compact rubidium-based optical frequency reference for operation on nanosatellites,” J. Opt. Soc. Am. B 38(6), 1885–1891 (2021). [CrossRef]
29. K. G. Libbrecht and J. L. Hall, “A low-noise high-speed diode laser current controller,” Rev. Sci. Instrum. 64(8), 2133–2135 (1993). [CrossRef]
30. B. Wiegand, “Linien - user-friendly spectroscopy locking,” https://hermitdemschoenenleben.github.io/linien/ (2020).
31. B. Wiegand, B. Leykauf, R. Jördens, and M. Krutzik, “A versatile, user-friendly, open-source fpga-based tool for jitter-tolerant frequency stabilization and optimization,” in preparation.
32. I. Newton, “VII. scala graduum caloris,” Philos. Trans. R. Soc. London 22(270), 824–829 (1701). [CrossRef]
33. M. Schmidt, M. Prevedelli, A. Giorgini, G. M. Tino, and A. Peters, “A portable laser system for high-precision atom interferometry experiments,” Appl. Phys. B 102(1), 11–18 (2011). [CrossRef]
34. Zynq-7000 SoC Data Sheet: Overview, XILINX (2018). V1.11.1.
35. P.-I. Schneider, X. Garcia Santiago, V. Soltwisch, M. Hammerschmidt, S. Burger, and C. Rockstuhl, “Benchmarking five global optimization approaches for nano-optical shape optimization and parameter reconstruction,” ACS Photonics 6(11), 2726–2733 (2019). [CrossRef]
36. Hewlett Packard, Englewood, CO, USA, Hints for making better microwave counter measurements, 1st ed. (1998).
37. A. Gusching, M. Petersen, N. Passilly, D. Brazhnikov, M. A. Hafiz, and R. Boudot, “Short-term stability of cs microcell-stabilized lasers using dual-frequency sub-doppler spectroscopy,” J. Opt. Soc. Am. B 38(11), 3254 (2021). [CrossRef]
38. V. Maurice, Z. L. Newman, S. Dickerson, M. Rivers, J. Hsiao, P. Greene, M. Mescher, J. Kitching, M. T. Hummon, and C. Johnson, “Miniaturized optical frequency reference for next-generation portable optical clocks,” Opt. Express 28(17), 24708 (2020). [CrossRef]
39. Z. L. Newman, V. Maurice, C. Fredrick, T. Fortier, H. Leopardi, L. Hollberg, S. A. Diddams, J. Kitching, and M. T. Hummon, “High-performance, compact optical standard,” Opt. Lett. 46(18), 4702 (2021). [CrossRef]
40. M. Hummon, D. Bopp, J. Kruse, A. Yulaev, D. Westly, K. Srinivasan, V. Aksyuk, and J. Kitching, “A dual beam photonic wavelength refernce,” Meas. Sensors 18, 100288 (2021). [CrossRef]
41. C. Glaser, F. Karlewski, J. Kluge, J. Grimmel, M. Kaiser, A. Günther, H. Hattermann, M. Krutzik, and J. Fortágh, “Absolute frequency measurement of rubidium 5s-6p transitions,” Phys. Rev. A 102(1), 012804 (2020). [CrossRef]
