Cell-based frequency references

Contact: R. Boudot (rodolphe.boudot@femto-st.fr)

Our group is involved in the study and development of Cs vapor cell atomic clocks and frequency references. These activities involve optics, laser spectroscopy, atomic physics, low-noise analog and digital electronics, MEMS and MOEMS technologies, time and frequency metrology. Our activities are divided into three main sections:

  1. Miniature CPT-based Cs cell atomic clocks: With the help of MEMS techniques, VCSEL lasers and integrated electronics, we develop miniature atomic clocks aiming to combine a low power consumption (150 mW), a small volume (15 cm3) and a fractional frequency stability better than 10-11 at 1 hour and 1 day integration (1 μs per day), in a large temperature range (-40 to +85°C). Such “pocket-size” atomic frequency references are dedicated to be an alternative to quartz-crystal oscillators in numerous applications including satellite-based navigation and positioning systems, telecommunication systems, defense systems. These activities are performed in strong collaboration with FEMTO-ST MOEMS Group [http://projects.femto-st.fr/MOEMS-Group/fr].
  2. High-performance compact CPT-based Cs cell atomic clock: We aim to explore the ultimate performances that can be achieved using the CPT technique for atomic clocks applications. The goal is to demonstrate a CPT-based Cs cell atomic clock, with similar size and power consumption than commercially-available Cs beam clocks, but with a short-term frequency stability 10-50 times better. Our laboratory-prototype clock, combining an optimized CPT pumping scheme named push-pull optical pumping (proposed by Happer’s group in Princeton, in 2004) and a pulsed Ramsey-based interrogation protocol, has recently demonstrated a short-term frequency stability at the level of 2 10-13 τ-1/2. With the implementation of an Auto-Balanced Ramsey interrogation protocol, the contribution of power-induced light shifts to the frequency stability has been strongly rejected in the 10-16 range at 10 000 s. Under quiet conditions and on a limited time scale of 30 000 s, the potential for this clock to reach the stability level of 2.5 10-15 at 10 000 s has been reported.
  3. MEMS-cell based optical frequency references: These activities aim to develop new-generation miniaturized optical frequency references based on the excitation and detection of high quality-factor optical resonances in MEMS vapor cells. The objective is to demonstrate ultimately fully-miniaturized optical frequency references with frequency stability performances 50-100 times better than CPT-based microwave miniature atomic clocks, for a reasonably increased size and power consumption.  In this domain, we have recently started the investigation and development of a Cs MEMS cell-based optical frequency reference based on an original dual-frequency sub-Doppler spectroscopy technique.


1/ Miniaturized CPT-based microwave atomic clocks 


       A/ Basics on CPT physics and CPT-based MAC architecture

Figure 1: CPT interaction in Cs atom represented by a 3- level Λ-scheme interacting with a bi-chromatic optical field. Both optical lines are frequency-split by 9.192 GHz (ground-state splitting), the CPT Cs clock transition. When the frequency difference between both optical lines exactly equals 9.192 GHz, atoms are optically-pumped in a coherent superposition of both ground states. In this so-called dark state, the transparency of the atomic vapor is increased, as shown on the right inset. The CPT resonance, with narrow line-width, can be used for the development of an atomic clock. In a CPT clock, the microwave interrogation signal is directly optically carried, preventing the use of a resonant cavity.

Basic blocks of a miniature atomic clock (MAC) are shown below on figure 2:

Figure 2: Schematic of CPT-based miniature Cs vapor cell atomic clock

The heart of a MAC is a micro-fabricated cell that contains alkali vapor, generally diluted with a pressure of buffer gas in order to slow down alkali atoms. Slight collisions between alkali atoms and buffer gas allow to increase the time for the atoms to reach the cell walls. This allows the detection of narrow CPT resonances (a few kHz line-width in mm-scale cell dimensions). The cell is typically heated at 80-95°C. A static magnetic field, parallel to the laser beam propagation direction, is applied to raise the Zeeman degeneracy. A magnetic shielding is used to prevent perturbations from the environment. Atoms in the cell interact with a laser beam coming from a VCSEL diode laser whose injection current is directly modulated at 4.596 GHz by a local oscillator to produce two first-order optical sidebands frequency-split by 9.192 GHz for CPT interaction. The laser beam is shaped, routed and polarized circularly with a quarter-wave plate. The light transmitted through the cell is detected by a photodiode. The output signal of the photodiode is used for various servo loops including in particular the laser frequency stabilization and the local oscillator frequency stabilization.

               

                 B/ Brief history of CPT-based MACs at FEMTO-ST

The study and development of CPT-based miniature atomic clocks has started at FEMTO-ST in 2005 (funding supports from CNES, Région de Franche-Comté and ANR). From 2008 to 2012, FEMTO-ST has piloted a European project called MAC-TFC (EC funding), combining the expertise of 10 industrial and academic partners (www.mac-tfc.eu). This project has led to the demonstration of a first European miniature atomic clock prototype. Main scientific achievements of this project were the development of custom-designed 894 nm (Cs D1 line at 894.6 nm) VCSEL diode lasers (Ulm University), the demonstration of 15-mW and low phase noise 4.596 GHz ASIC synthesizers devoted to be used as local oscillator (EPFL-IMT), and the development of an original Cs vapor microcell technology (FEMTO-ST/SAES/Wroclaw University). This stimulating project led to the beginning in France of new projects (supports from DGA, LabeX FIRST-TF, ANR, BPI). In 2014, a French industrial-academic platform has been implemented in order to develop an industrial miniature atomic clock.

             C/ Cs vapor microcell technology

We have proposed and developed at FEMTO-ST an original Cs vapor microcell technology. This cell consists of a DRIE-etched silicon substrate sandwiched between two anodically-bonded glass wafers. The cell contains two cavities. The first cavity contains a pill Cs dispenser. The second cavity is the cavity in which CPT interaction takes place. Both cavities are connected by filtration channels. The originality of this cell technology is that Cs vapor is generated after complete sealing of the cell by local laser activation of the Cs pill dispenser.

Figure 3 shows a photograph of Cs microfabricated cells developed in FEMTO-ST. This cell technology is called T-cell.

Figure 3: Photographs of Cs vapor microfabricated cells. The Cs dispenser is visible in the square cavity. Courtesy from FEMTO-ST MOEMS Group.

Figure 4: Example of a CPT resonance detected in a Cs-Ne microfabricated cell.

In 2015, we reported an original Cs microcell architecture, named R-cell, designed for miniature atomic clocks. This cell combines diffraction gratings with anisotropically etched single-crystalline silicon sidewalls to route a normally-incident beam in a cavity oriented along the substrate plane.

Figure 5: Photograph of the R-cell architecture. Courtesy from FEMTO-ST MOEMS Group.

In 2017, we have proposed and reported a method for filling alkali vapor cells with cesium from a dispensing paste, compatible with collective deposition processes. This filling method could reduce the cost and the complexity of miniature cells fabrication. Optical linear spectroscopy was performed over one year on such cells, showing a stable atomic density. One of these cells has been implemented in a lab-prototype CPT clock. A fractional frequency aging rate of about –4.4 10-12 per day has been measured, compliant with typical objectives of MACs.

In 2018, in collaboration with our industrial partner Tronics Microsystems, we have reported the characterization of Cs vapor microcells based on pill dispensers and fabricated in a MEMS foundry, according to a process compatible with mass-production. More than three quarters of cells from 6-inch wafers are successfully filled with Cs vapor. Various cells of a given wafer have been characterized using CPT spectroscopy, demonstrating similar buffer gas (Ne) pressure with a standard deviation of about 2.5% and CPT resonances with similar line-width and contrast properties. In addition, frequency drifts mainly attributed to cell inner atmosphere variations have been investigated onto several cells over 250-500 hour measurements. The corresponding contribution at 1 day averaging time to the clock fractional frequency stability is estimated to be about 10-11 or lower. The fractional frequency stability of a clock prototype using such an industrial Cs-Ne microcell was measured to be 2.5 10-11 τ-1/2 up to 200 s averaging time, and better than 2 10-11 at 105 s. These performances tend to demonstrate that this vapor cell technology, compatible with mass-production, is suitable for industrial miniature quantum clocks or sensors.

In 2019, we reported a study on the mitigation of light-shift effects in miniaturized atomic clocks through the implementation of additional electronics stabilization loops. The first loop stabilizes the actual temperature of the VCSEL chip using a compensation method. The second loop stabilizes the total microwave power absorbed by the laser to a value that maximizes the optical absorption and reduces the clock frequency dependence to laser-power variations.

                    D/ MEMS-based BAW-resonator oscillators

Usually, the local oscillator of a MAC is a voltage controlled oscillator (VCO) phase locked to a 10 MHz quartz crystal oscillator using a fractional phase locked loop (PLL). As a possible alternative solution, we have investigated the development and characterization of MEMS-based oscillators based on bulk acoustic wave (BAW) resonators, including solid mounted resonators (SMR) or high-overtone bulk acoustic wave resonators (HBAR). Such resonators exhibit high Q-f factors, low residual phase noise, miniaturized dimensions and low power consumption.

In 2011, we have demonstrated, in collaboration with IEMN and CEA-LETI, the development and the use of a SMR-based oscillator for miniature atomic clocks applications.

In 2014-2016, we have reported the characterization of 2.3 GHz AlN-Sapphire high-overtone bulk acoustic resonators (HBARs), with a typical loaded Q-factor of 25 000, 15–20 dB insertion loss, and resonances separated by about 10 MHz. The temperature coefficient of frequency of these HBARs was measured to be about -25 ppm/K. A significant distortion of the HBAR resonance line-shape, attributed to non-linear effects, has been observed at high input microwave power. The power-induced fractional frequency variation of the HBAR resonance was measured. The residual phase noise of a HBAR was measured in the range of -110 to -130  dBrad2/Hz at 1Hz Fourier frequency, yielding an ultimate HBAR-limited oscillator Allan deviation of about 7 10-12  at 1 s integration time. A HBAR resonator was used for the development of a low phase noise 2.3 GHz oscillator, yielding an absolute phase noise of -60, -120, and -145 dBrad2/Hz for offset frequencies of 10 Hz, 1 kHz, and 10 kHz, respectively, in excellent agreement with the Leeson effect. Such a HBAR oscillator has been used as a local oscillator in a microcell CPT-based atomic clock.

Figure 6: Photograph of a AlN-Sapphire HBAR resonator (designed by CEA-LETI).

Figure 7: Phase noise performances of a 2.3 GHz HBAR oscillator (in red). Performances compared to those of a conventional MAC LO or to state-of-the-art ideally frequency-multiplied 100 MHz OCXO.

             E/ VCSELs

VCSEL laser sources combine a low threshold current, low power consumption and high-modulation bandwidth capabilities and are well-adapted to be used in miniature atomic clocks. In the frame of the MAC-TFC project, in collaboration with Ulm University and LTF-UNINE, we have reported the metrological characterization of custom-designed 894nm VCSELs. More recently, we have also reported the characterization of recent commercially-available 894 nm VCSELs.


           F/ Laboratory-prototype clocks

Figure 8 shows a microcell-based compact atomic clock physics package developed in the frame of the MAC-TFC project. Figure 9 shows this physics package embedded onto the pilot electronics card (developed by EPFL).

Figure 8: Picture of the MAC-TFC clock physics package.

Figure 9: Picture of the MAC-TFC clock. The physics package is connected to electronics to operate the clock. Electronics were developed by EPFL-IMT.

We have recently developed a novel MAC prototype for lab works and graduate students. The clock physics package and electronics of the clock has been developed in FEMTO-ST. This prototype is used during EFTS seminars (http://efts.eu/dokuwiki/doku.php?id=current:01_program ).

Figure 10: Miniature clock prototype. Courtesy of J. Rutkowski and V. Maurice.

            G/ Pulsed Ramsy-based CPT spectroscopy in microfabricated cells.

Pulsed coherent population trapping (CPT) spectroscopy has been applied in buffer-gas filled Cs–Ne vapor micro-fabricated cells. Figure 11 depicts an example of Ramsey-CPT fringes detected in a Cs-Ne microcell. The properties of the Ramsey-CPT clock transition central fringe (line-width, signal amplitude, and contrast) were studied versus several experimental parameters, including the Ramsey sequence and the input laser intensity, and were compared to those obtained in the conventional continuous (CW) interrogation mode. In the pulsed case and for short Ramsey-free evolution times TR, the central fringe line-width is found to exhibit a small but visible power broadening and is measured to be narrower than the value of 1∕(2TR) that is reached for long TR. The microwave hyperfine coherence lifetime T2 in the Cs–Ne microcells is measured to be in the 50–500 μs range. Such studies could be interesting for the development of future chip-scale atomic clocks, operating in the pulsed regime.

Figure: Typical CPT resonance detected in the CW regime (black) and in the pulsed Ramsey-CPT regime (red), in a Cs-Ne MEMS cell.

2/ High-performance CPT-based Cs cell atomic clock

In 2011, in collaboration with LNE-SYRTE (S. Guérandel and E. de Clercq), we started the development of a high-performance CPT-based Cs cell atomic clock. Funded in the beginning by LNE, these activities have been pursued from 2013 to 2016 in the frame of a European project called MClocks, funded by EURAMET, and piloted by INRIM (coordinator: S. Micalizio). This project has been supported later by LabeX FIRST-TF. 

Our high-performance CPT clock combines an optimized CPT pumping scheme, named  push-pull optical pumping (PPOP), pioneerly proposed by Y. Y. Jau et al. in 2004 (Happer's group, Princeton, Phys. Rev. Lett. 93, 16, 2004) and  a pulsed Ramsey-based interrogation protocol, yielding the detection of high-contrast Ramsey-CPT fringes. Our laboratory-prototype clock uses now a sophisticated Auto-Balanced Ramsey interrogation protocol, pioneerly proposed for optical clocks in PTB, Germany (see C. Sanner et al., Phys. Rev. Lett. 2018). This method allows the drastic reduction of light-shift effects. This CPT clock demonstrates to date a fractional frequency stability at the level of 2 10-13 τ-1/2 up to 10 000 s, reaching the level of 2.5 10-15 at 104 s. To our knowledge, these performances are the best performances ever reported for a CPT-based atomic clock.

                          A/ Architecture of the CPT clock

Figure 12 shows the architecture of the Ramsey-CPT clock. It combines a DFB laser source tuned on the Cs D1 line, a fibered electro-optic modulator driven by a 4.596 GHz low noise microwave signal for generation of the CPT sidebands, an AOM for laser power stabilization and production of the Ramsey sequence and a Michelson delay-line and polarization orthogonalizer system for the generation of the PPOP scheme. The light is sent into a 5-cm long and 2-cm diameter buffer-gas filled Cs cell. The light at the output of the cell is detected by a photodiode. The output signal is exploited by a FPGA-based digital electronics board (developed by C. Calosso, INRIM) that generates the Ramsey sequence pattern and manages different servo loops. The local oscillator is an ultra-low phase noise 100 MHz OCXO frequency-multiplied to 4.596 GHz. The output signal of the 100 MHZ OCXO is at the end compared to a hydrogen maser for stability measurements.

Figure 12: Schematic of the Ramsey-CPT clock

ramsey fringe

Figure 13: Example of Ramsey-CPT fringes. The line-width of the central fringe equals 1/(2T), with T the free-evolution time in the Ramsey-CPT sequence.

                B/ Ultra-low noise microwave frequency synthesizers

In collaboration with INRIM (C. Calosso/S. Micalizio), we have developed ultra-low phase noise microwave frequency synthesizers at 4.596 GHz or 9.192 GHz, dedicated to be used as local oscillators in high performance Cs (or Rb) vapor cell atomic clocks. Such microwave sources allow to reduce greatly the Dick effect contribution (3 10-14 at 1 s) to the short-term frequency stability of the atomic frequency standards. This level is comparable with the photon shot noise limit.

Figure 14: Photograph of a microwave frequency synthesizer developed by FEMTO-ST / INRIM [B. Francois, C. Calosso, R. Boudot].

Figure 15: Absolute phase noise performances of the microwave frequency synthesizer shown above. The pilot is a low noise 100 MHz OCXO (perfs in red at 100 MHz). The green data shows the absolute phase noise at 4.596 GHz. The green line is the phase noise at 4.596 GHz of the ideally frequency-multiplied 100 MHz OCXO.

                          C/ Reduction of light-shift effects with Auto-Balanced Ramsey (ABR) interrogation protocol

Vapor-cell atomic clocks are widely appreciated for their excellent short-term fractional frequency stability and their compactness. However, they are known to suffer on medium and long time scales from significant frequency instabilities, generally attributed to light-induced frequency-shift effects.

In order to tackle this limitation, we have investigated the application of the Auto-Balanced Ramsey (ABR) interrogation protocol (see C. Sanner et al., Phys. Rev. Lett. 120, 053602 (2018)) onto our CPT-based pulsed hot-vapor Cs vapor-cell clock.

We have demonstrated that the ABR protocol, developed initially to probe the one-photon resonance of quantum optical clocks, can be successfully applied to a two-photon CPT resonance. The applied method, based on the alternation of two successive Ramsey-CPT sequences with unequal free-evolution times and the subsequent management of two interconnected phase and frequency servo loops, allows a relevant reduction of the clock-frequency sensitivity to light-shift effects.

This ABR-CPT protocol, improved further later with symmetrization (SABR-CPT), has allowed a drastic reduction of the clock frequency sensitivity to laser power variations, by a factor 80 in comparison with the standard Ramsey-CPT regime. This technique has reduced the contribution of the laser power-shift effect on the clock frequency stability to the level of a few 10-16 at 104 s.

Figure 18: Symmetric ABR-CPT sequence. 

Figure 19 reports the Allan deviation of the clock in different conditions. The curve (a) shows the best performances ever obtained in the Ramsey-CPT regime. The curve (b) shows first results obtained in the ABR-CPT regime. The curve (c), extracted from a 5-days measurement, is obtained in the SABR-CPT regime, without compensation of the laser AM noise (explaining the degradation of the short-term stability). The curve (d), extracted from a 30 000 s data set with quiet experimental conditions, is obtained in the SABR-CPT regime, with additional compensation of the laser AM noise. In the last case, the clock demonstrates a clock fractional frequency stability of 2 10-13 τ-1/2, until almost 104 s, reaching the level of 2.5 10-15 at 104 s.

Figure 19: Allan deviation of the clock. (a) Ramsey-CPT, (b) First results obtained in the ABR-CPT regime, (c): SABR-CPT: extracted from a 5-days measurement, without compensation of the laser AM noise, (d): SABR-CPT, extracted from a 30 000 s data set with quiet experimental conditions, with additional compensation of the laser AM noise for improvement of the short-term stability. In the last case, the clock demonstrates a clock fractional frequency stability of 2 10-13 τ-1/2, until almost 104 s, reaching the level of 2.5 10-15 at 104 s.

              D/ Annex studies: Wall coated Cs vapor cells.

We have reported the realization and characterization using coherent population trapping (CPT) spectroscopy of octa-decyl-trichlorosilane (OTS)-coated centimeter-scale Cs vapor cells. The dual-structure of the resonance line-shape, with presence of a narrow structure line at the top of a Doppler-broadened structure, was clearly observed. The line-width of the narrow resonance was compared to the line-width of an evacuated Cs cell and of a buffer gas Cs cell of similar size. The Cs-OTS adsorption energy was measured to be (0.42+/-0.03) eV, with a clock frequency shift rate of 2.710-9/K in fractional unit. A hyperfine population lifetime, T1, and a microwave coherence lifetime, T2, of 1.6 and 0.5 ms were reported, corresponding to about 37 and 12 useful bounces, respectively.

Figure 20: Photograph an OTS-coated cell.

Figure 21: CPT resonance in a Cs-OTS cell (compared to a pure Cs cell of similar dimensions).

3/ MEMS-cell optical frequency references

The exploration of innovative approaches combining advanced quantum physics concepts, hybrid integration of MEMS cell technologies and on-chip photonics devices, and high-performance digital electronics constitutes an exciting research path towards the development of new-generation miniaturized optical atomic clocks.

FEMTO-ST has recently reported the detection of high-contrast sub-Doppler resonances in Cs MEMS vapor cells using an original  dual-frequency sub-Doppler spectroscopy (DFSDS) technique.  In this system, alkali thermal atoms confined in a mm-scale vapor cell interact with two orthogonally-polarized counter-propagating dual-frequency optical fields, yielding the detection of high-contrast sign-reversed sub-Doppler optical resonances. The observation of these enhanced-absorption spikes has been explained in an extended theoretical model (established in collaboration with D. Brazhnikov from Institute of Laser Physics, Novosibirsk, Russia) through the contribution of Zeeman dark states, hyperfine dark states and optical pumping effects.   

Figure 16 shows the architecture of the MEMS cell based optical frequency reference.

Figure 16: Dual-frequency sub-Doppler spectroscopy setup.

Fgure 17 reports high-contrast sub-Doppler absorption spikes in a hot atomic vapor cell exposed to a dual-frequency laser field. Similar high-contrast resonances have been detected in mm-scale Cs vapor cells.

Figure 17: High-contrast sub-Doppler absorption spikes in a hot atomic vapor cell exposed to a dual-frequency laser field.

These high-Q factor (Q~5 10^7) optical resonances have been recently used for frequency stabilization of a diode laser, yielding a short-term frequency stability lower than 2 10-12 τ-1/2 until 10 s integration time. These promising  performances are about 50-100 times better than those of commercial microwave CPT-based chip-scale atomic clocks [20] and demonstrate the interest of this approach for the development of new-generation fully-miniaturized cell-based optical frequency references. Combined with integrated on-chip microresonator-based optical frequency combs used as optical-to-microwave frequency dividers, this clock architecture could constitute the basis for the generation of ultra pure microwave signals in a compact system with reasonable size and power consumption.

 Publications

    1. D. Miletic, P. Dziuban, R. Boudot, M. Hasegawa, R. K. Chutani, G. Mileti, V. Giordano and C. Gorecki, Electron. Lett. 46, 15, 1069-1071 (2010).
    2. R. Boudot, P. Dziuban, M. Hasegawa, R. Chutani, S. Galliou, V. Giordano and C. Gorecki, Journ. Appl. Phys. 109, 014912 (2011).
    3. M. Hasegawa, R. K. Chutani, C. Gorecki, R. Boudot, P. Dziuban, V. Giordano, S. Clatot, J. Dziuban and L. Mauri, Sensors Actuators A - Phys. 167, 594-601 (2011).
    4. R. Boudot, D. Miletic, P. Dziuban, P. Knapkiewicz, J. Dziuban, C. Affolderbach, G. Mileti, V. Giordano and C. Gorecki, Optics Express 19, 4, 3106-3114 (2011).
    5. R. Boudot, M. D. Li, V. Giordano, N. Rolland, P. A. Rolland, P. Vincent, Rev. Sci. Instr. 82, 034706 (2011).
    6. O. Kozlova, R. Boudot, S. Guerandel and E. De Clercq, IEEE Trans. Instrum. Meas. 60, 7, 2262-2266 (2011).
    7. D. Miletic, C. Affolderbach, M. Hasegawa, R. Boudot, C. Gorecki and G. Mileti, Appl. Phys. B: Lasers Opt. 109, 89–97 (2012).
    8. X. Liu and R. Boudot, IEEE Trans. Instr. Meas. 61, 10, 2852-2855 (2012).
    9. R. Boudot, X. Liu, P. Abbé, R. K. Chutani, N. Passilly, S. Galliou, C. Gorecki and V. Giordano, IEEE Trans. Ultrason. Ferroelec. Freq. Contr. 59, 11, 2584-2587 (2012).
    10. R. Boudot and E. Rubiola, IEEE Trans. Ultrason. Ferroelec. Freq. Contr. 59, 12, 2613-2624 (2012).
    11. X. Liu, J. M. Merolla, S. Guérandel, C. Gorecki, E. De Clercq and R. Boudot, Phys. Rev. A 87, 013416 (2013).
    12. F. Gruet, E. Kroemer, L. Bimboes, D. Miletic, C. Affolderbach, A. Al-Samaneh, D. Wahl, R. Boudot, G. Mileti and R. Michalzik, Optics Express 21, 5, 5781-5792 (2013).
    13. X. Liu, J.M. Merolla, S. Guérandel, E. De Clercq and R. Boudot, Optics Express 21, 10, 12451-12459 (2013).
    14. M. Hasegawa, R. K. Chutani, R. Boudot, L. Mauri, C. Gorecki, X. Liu and N. Passilly, J. Micromech. Microeng. 23, 055022 (2013).
    15. R. Salut, C. Gesset, G. Martin, B. Assouar, P. Bergonzo, R. Boudot, O. Elmazria and S. Ballandras, Elsevier, Microelectron. Eng. 112, 133-138 (2013).
    16. J. M. Friedt, R. Boudot, G. Martin and S. Ballandras, Rev. Sci. Instr. 85, 094704 (2014).
    17. B. François, J-M. Danet, C. E. Calosso and R. Boudot, Rev. Sci. Instr. 85, 094709 (2014).
    18. M. Abdel Hafiz, V. Maurice, R. Chutani, N. Passilly, C. Gorecki, S. Guérandel, E. De Clercq and R. Boudot, Journ. Appl. Phys. 117, 184901 (2015).
    19. E. Kroemer, M. Abdel Hafiz, V. Maurice, B. Fouilland, C. Gorecki and R. Boudot, Opt. Express 23, 14, 18373-18380 (2015).
    20. R. K. Chutani, V. Maurice, N. Passilly, C. Gorecki, R. Boudot, M. Abdel Hafiz, P. Abbé, S. Galliou, J. Y. Rauch and E. De Clercq, Nature Sci. Rep. 5, 14001 (2015).
    21. B. Francois, C. E. Calosso, M. Abdel Hafiz, S. Micalizio and R. Boudot, Rev. Sci. Instr. 86, 094707 (2015).
    22. M. Abdel Hafiz and R. Boudot, Journ. Appl. Phys. 118, 124903 (2015).
    23. T. Daugey, J. M. Friedt, G. Martin and R. Boudot, Rev. Sci. Instr. 86, 114703 (2015).
    24. M. Abdel Hafiz, G. Coget, E. De Clercq and R. Boudot, Opt. Lett. 41, 13, 2982-2985 (2016).
    25. M. Abdel Hafiz, X. Liu, S. Guérandel, E. De Clercq and R. Boudot, Journal of Physics: Conference Series, 723 (1), 012013 (2016).
    26. E. Kroemer, J. Rutkowski, V. Maurice, R. Vicarini, M. Abdel Hafiz, C. Gorecki and R. Boudot, Applied Optics 55, 31, 8839-8847 (2016).
    27. R. Boudot, G. Martin, J. M. Friedt and E. Rubiola, Journal of Applied Physics 120, 224903 (2016).
    28. P. Yun, F. Tricot, C. E. Calosso, S. Micalizio, B. Francois, R. Boudot, S. Guérandel and E. de Clercq, Phys. Rev. Applied7, 014018 (2017).
    29. M. Abdel Hafiz, G. Coget, P. Yun, S. Guérandel, E. De Clercq and R. Boudot, Journal of Applied Physics 121, 104903 (2017).
    30. V. Maurice, J. Rutkowski, E. Kroemer, S. Bargiel, N. Passilly, R. Boudot, C. Gorecki, L. Mauri and M. Moraja, Appl. Phys. Lett. 110, 164103 (2017).
    31. M. Abdel Hafiz, D. Brazhnikov, G. Coget, A. Taichenachev, V. I. Yudin, E. De Clercq and R. Boudot, New Journal of Physics 19, 073028 (2017).
    32. R. Boudot, V. Maurice, C. Gorecki and E. de Clercq, Journal of Optical Society America B 35, 5, 1004-1010 (2018). https://doi.org/10.1364/JOSAB.35.001004 
    33. D. Brazhnikov, G. Coget, M. Abdel Hafiz, V. Maurice, C. Gorecki and R .Boudot, IEEE Transactions Ultrasonics Ferroelectrics Frequency Control 65, 6, 962-972 (2018). https://doi.org/10.1109/TUFFC.2018.2811319
    34. M. Abdel Hafiz, G. Coget, M. Petersen, C. Rocher, S. Guérandel, T. Zanon-Willette, E. de Clercq and R. Boudot, Physical Review Applied 9, 064002 (2018). https://doi.org/10.1103/PhysRevApplied.9.064002 
    35. M. Abdel Hafiz, G. Coget, M. Petersen, C. Calosso, S. Guérandel, E. de Clercq and R. Boudot, Applied Physics Letters 112, 244102 (2018). https://doi.org/10.1063/1.5030009
    36. R. Vicarini, V. Maurice, M. Abdel Hafz, J. Rutkowski, C. Gorecki, N. Passilly, L. Ribetto, V. Gaff, V. Volant, S. Galliou and R. Boudot, Sensors Actuators, Phys. A 280, 99-106 (2018). https://doi.org/10.1016/j.sna.2018.07.032
    37. V. I. Yudin, A. Taichenachev, M. Yu Basalaev, T. Zanon-Willette, T. E. Mehlstauber, R. Boudot, J. W. Pollock, M. Shuker, E. A. Donley and J. Kitching, New Journal of Physics 20, 123016 (2018). https://doi.org/10.1088/1367-2630/aaf47c
    38. D. Brazhnikov, M. Petersen, G. Coget, V. Maurice, N. Passilly, C. Gorecki and R. Boudot, Phys. Rev. A 99, 062508 (2019). https://doi.org/10.1103/PhysRevA.99.062508
    39. R. Vicarini, M. Abdel Hafiz, V. Maurice, N. Passilly, E. Kroemer, L. Ribetto, V. Gaff, C. Gorecki, S. Galliou and R. Boudot, Mitigation of temperature-induced light-shift effects in miniaturized atomic clocks,  IEEE Transactions on Ultrasonics Ferroelectrics and Frequency Control 66, 12, 1962-1967 (2019). https://doi.org/10.1109/TUFFC.2019.2933051

    40. M. Shuker, J. W. Pollock, R. Boudot, V. I. Yudin, A. V. Taichenachev, J. Kitching and E. A. Donley, Physical Review Letters 122, 113601 (2019). https://doi.org/10.1103/PhysRevLett.122.113601

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