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Studies on miniature and compact Ramsey double-resonance Rubidium atomic clocks using hot vapors and cold atoms

Etienne Batori

Published Jan 1, 2023• 0 citations
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Abstract

This thesis presents results on two microwave, double-resonance, Rubidium 87 atomic clocks. These studies are motivated by the need for compact and miniature clocks with improved performances or improved Size,Weight and Power (SWaP). A first clock study, covered in chapter 3, focuses on the μPOP clock, the first demonstration of Double Resonance (DR) Ramsey operation in a micro-manufactured hot-vapor cell clock.With a short-termstability of σy(τ ) ≤ 2 × 10−11τ−1/2 and long-termstability of 1.5 × 10−12 at one day, the μPOP clock features state-of-the-art stability for microwave miniature cell clocks. As demonstrated in [1], the μPOP clock short-term stability has been optimized to mitigate the Dick effect and laser Relative Intensity Noise (RIN) contributions, with the latter being the biggest contributor to the short-termstability. The long-terminstability budget shows that the intensity and frequency light shifts contributions are one and two order of magnitudes lower than the measured stability with a contribution of the order of 10−13 and 10−14 at one day, respectively. This confirms the interest of the Pulsed Optically Pumped (POP) approach compared to the ContinuousWave (CW) scheme and sets the potential performances of the μPOP clock. Other long-termcontributors to the instabilities have been evaluated. In the upper limit, the contribution of the cell-temperature shift to the instability is estimated to be two orders of magnitude below the measured stability, confirming the benefit of the N2 and Ar buffer gas-mixture approach for a close to zero cell-temperature sensitivity coefficient. The last two effects, the microwave-power and the position shifts are the greatest contributor to the mid and long-termstability with the latter being the limiting long-term phenomenon whose contribution must be carefully evaluated using the Groslambert covariance. The μPOP studies conclude with the description of a fast and reliable method for measuring the relaxation rates in Ramsey DR vapor-cell clocks. At the nominal cell temperature, namely ≈ 100◦C, the population and coherence relaxations rates are measured to be at the order of 5 kHz and 4 kHz, respectively. Their values have been measured down to 60◦C with both at the order of 1 kHz. Finally, a theoretical model using only parameters taken from the literature has been derived to describe the measured relaxation rates values with agreement within 20%. Chapter 4 focuses on the simulation and realization of a microwave cavity for a DR cold-atom clock using a GratingMagneto-Optical Trap (GMOT). The final cavity shows a low quality factor of Q ≈ 360 which is in the interest of reducing the cavity-pulling shift. The TE011-like cavity mode is separated by at least 500 MHz from the neighbouring modes as predicted by the simulations. The same simulations allowed to effectively predict the cavity’s resonance frequency with a small error of 60 MHz which can easily be compensated by the cavity frequency tuning mechanism. The expected simulated excellent properties of the resonance mode in termof microwave field uniformity and homogeneity are confirmed by measurement of the field field orientation factor of 97% and low Rabi oscillation damping, respectively. Chapter 5 focuses on the integration of the microwave cavity in a clock setup designed by Erling Riis group from the university of Strathclyde. The clock described in this chapter is the first realization of a DR Ramsey Rb cold-atom clock using a GMOT for cooling and trapping which reduces the clock footprint. In practise, ≈ 106 atoms at ≈ 10 μK are loaded thanks to the grating. Ramsey fringes were successfully obtained with Ramsey times up to 20 ms, limited by the clock geometric design. The clock implements state-selection that allows for increased Signal-to-Noise Ratio (SNR) and better short-term stability of ≈ 1.5 × 10−11τ−1/2. This stability is well-explained by SNR of the fringes. Long-term stability is dominated by the 2nd-order Zeeman shift contribution as the clock is not magnetically shielded. The two studies presented in this thesis, namely the μPOP and cold-atom clocks, pave the way towards more miniature and compact frequency standards, respectively. Further improvements of the former would yield a intensity light shift limited clock with ≈ 10−13 stability at one day. Further version of the latter clock using the cavity as standalone vacuum system would allow for reduced SWaP cold-atom frequency standards.

DOI
10.35662/unine-thesis-3067

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We demonstrate and study a microcell microwave atomic clock based on optical-microwave double resonance (DR) interrogation operated in a pulsed Ramsey scheme, called the \ensuremath{\mu}POP clock, based on a microfabricated Rb vapor cell and a micro-loop-gap microwave resonator. For the mm-scale dimensions of this cell, the population and coherence relaxation rates of the Rb clock transition are on the order of 4--5 kHz, which puts constraints on the useful Ramsey times and overall pulse sequence in view of optimized clock performance. Our proof-of-principle demonstration of the \ensuremath{\mu}POP clock shows that the pulsed DR approach is nevertheless feasible and results in a short-term clock stability of 1 \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}11}$ \ensuremath{\tau}${}^{\ensuremath{-}1/2}$ and reaching the \ensuremath{\le}2 \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}12}$ level at timescales of 1000 s to one day. The short-term instability budget established for the \ensuremath{\mu}POP clock shows that the main limitation to the short-term stability arises from the detection noise. Thanks to the pulsed Ramsey scheme, light-shift effects are strongly reduced in the \ensuremath{\mu}POP clock, which opens perspectives for further improvements of long-term clock stability, in view of future generations of miniature vapor-cell clocks with enhanced performances based on the DR scheme.

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This thesis presents results on two microwave, double-resonance, Rubidium 87 atomic clocks. These studies are motivated by the need for compact and miniature clocks with improved performances or improved Size,Weight and Power (SWaP). A first clock study, covered in chapter 3, focuses on the μPOP clock, the first demonstration of Double Resonance (DR) Ramsey operation in a micro-manufactured hot-vapor cell clock.With a short-termstability of σy(τ ) ≤ 2 × 10−11τ−1/2 and long-termstability of 1.5 × 10−12 at one day, the μPOP clock features state-of-the-art stability for microwave miniature cell clocks. As demonstrated in [1], the μPOP clock short-term stability has been optimized to mitigate the Dick effect and laser Relative Intensity Noise (RIN) contributions, with the latter being the biggest contributor to the short-termstability. The long-terminstability budget shows that the intensity and frequency light shifts contributions are one and two order of magnitudes lower than the measured stability with a contribution of the order of 10−13 and 10−14 at one day, respectively. This confirms the interest of the Pulsed Optically Pumped (POP) approach compared to the ContinuousWave (CW) scheme and sets the potential performances of the μPOP clock. Other long-termcontributors to the instabilities have been evaluated. In the upper limit, the contribution of the cell-temperature shift to the instability is estimated to be two orders of magnitude below the measured stability, confirming the benefit of the N2 and Ar buffer gas-mixture approach for a close to zero cell-temperature sensitivity coefficient. The last two effects, the microwave-power and the position shifts are the greatest contributor to the mid and long-termstability with the latter being the limiting long-term phenomenon whose contribution must be carefully evaluated using the Groslambert covariance. The μPOP studies conclude with the description of a fast and reliable method for measuring the relaxation rates in Ramsey DR vapor-cell clocks. At the nominal cell temperature, namely ≈ 100◦C, the population and coherence relaxations rates are measured to be at the order of 5 kHz and 4 kHz, respectively. Their values have been measured down to 60◦C with both at the order of 1 kHz. Finally, a theoretical model using only parameters taken from the literature has been derived to describe the measured relaxation rates values with agreement within 20%. Chapter 4 focuses on the simulation and realization of a microwave cavity for a DR cold-atom clock using a GratingMagneto-Optical Trap (GMOT). The final cavity shows a low quality factor of Q ≈ 360 which is in the interest of reducing the cavity-pulling shift. The TE011-like cavity mode is separated by at least 500 MHz from the neighbouring modes as predicted by the simulations. The same simulations allowed to effectively predict the cavity’s resonance frequency with a small error of 60 MHz which can easily be compensated by the cavity frequency tuning mechanism. The expected simulated excellent properties of the resonance mode in termof microwave field uniformity and homogeneity are confirmed by measurement of the field field orientation factor of 97% and low Rabi oscillation damping, respectively. Chapter 5 focuses on the integration of the microwave cavity in a clock setup designed by Erling Riis group from the university of Strathclyde. The clock described in this chapter is the first realization of a DR Ramsey Rb cold-atom clock using a GMOT for cooling and trapping which reduces the clock footprint. In practise, ≈ 106 atoms at ≈ 10 μK are loaded thanks to the grating. Ramsey fringes were successfully obtained with Ramsey times up to 20 ms, limited by the clock geometric design. The clock implements state-selection that allows for increased Signal-to-Noise Ratio (SNR) and better short-term stability of ≈ 1.5 × 10−11τ−1/2. This stability is well-explained by SNR of the fringes. Long-term stability is dominated by the 2nd-order Zeeman shift contribution as the clock is not magnetically shielded. The two studies presented in this thesis, namely the μPOP and cold-atom clocks, pave the way towards more miniature and compact frequency standards, respectively. Further improvements of the former would yield a intensity light shift limited clock with ≈ 10−13 stability at one day. Further version of the latter clock using the cavity as standalone vacuum system would allow for reduced SWaP cold-atom frequency standards.
We demonstrate and study a microcell microwave atomic clock based on optical-microwave double resonance (DR) interrogation operated in a pulsed Ramsey scheme, called the \ensuremath{\mu}POP clock, based on a microfabricated Rb vapor cell and a micro-loop-gap microwave resonator. For the mm-scale dimensions of this cell, the population and coherence relaxation rates of the Rb clock transition are on the order of 4--5 kHz, which puts constraints on the useful Ramsey times and overall pulse sequence in view of optimized clock performance. Our proof-of-principle demonstration of the \ensuremath{\mu}POP clock shows that the pulsed DR approach is nevertheless feasible and results in a short-term clock stability of 1 \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}11}$ \ensuremath{\tau}${}^{\ensuremath{-}1/2}$ and reaching the \ensuremath{\le}2 \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}12}$ level at timescales of 1000 s to one day. The short-term instability budget established for the \ensuremath{\mu}POP clock shows that the main limitation to the short-term stability arises from the detection noise. Thanks to the pulsed Ramsey scheme, light-shift effects are strongly reduced in the \ensuremath{\mu}POP clock, which opens perspectives for further improvements of long-term clock stability, in view of future generations of miniature vapor-cell clocks with enhanced performances based on the DR scheme.
This thesis presents experimental studies on continuous-wave (CW) laser-microwave double-resonance (DR) spectroscopy and metrology in rubidium (87Rb) vapor cells in view of new high-performance, compact Rb-cell atomic clocks. The Rb vapor cell is confined inside a magnetron-type cavity microwave resonator (MWR). The CW DR spectroscopy involves two resonant electromagnetic fields that are operated simultaneously to interrogate the atoms - the optical field to polarize the atoms by optical pumping, and the microwave field to drive the ground-state hyperfine clock transition that serves as an atomic frequency reference. Details on characterization of compact laser heads and microwave synthesizers used in this work are presented. The vapor cell standards are useful in our everyday lives for applications ranging from telecommunications, navigation, metrology etc. In view of improving the performances of the Rb cell standards, two different clock approaches were studied in detail: The first one is on use of vapor cells (1.4 cm3) whose inner walls are coated with anti-relaxation material. A first ever wall-coated cell clock was demonstrated with good short-term frequency stability. The medium- to long-term stability was found to be limited by the temperature coefficient (TC) of the coating material itself. This work gave the insight to important features to be considered in future anti-relaxation coating materials for atomic standards. The second novel approach involves using a bigger cell (12 cm3) within a newly developed, improved MWR towards a high-performance atomic standard. Adopting a larger cell gives a higher atomic Q-factor signal that improves the short-term clock stability. In this approach, the cell was filled with 87Rb and buffer gases. With this clock, we demonstrate the state-of-the-art short-term stability of <1.4×10−13 τ−1/2. Metrological quantitative measurements on parameters influencing the medium- to long-term stability were studied in view of next generation satellite navigation systems that demand a stability level of <1×10−14 at 10 4 s (equivalent to <1 ns/day). The potential of short-term stability and understanding of the limiting factors on medium- to long-term time scales demonstrated in this study pave the way for future work towards the commercialization of high-performance Rb atomic clocks for a variety of applications.
This thesis presents experimental studies on continuous-wave (CW) laser-microwave double-resonance (DR) spectroscopy and metrology in rubidium (87Rb) vapor cells in view of new high-performance, compact Rb-cell atomic clocks. The Rb vapor cell is confined inside a magnetron-type cavity microwave resonator (MWR). The CW DR spectroscopy involves two resonant electromagnetic fields that are operated simultaneously to interrogate the atoms - the optical field to polarize the atoms by optical pumping, and the microwave field to drive the ground-state hyperfine clock transition that serves as an atomic frequency reference. Details on characterization of compact laser heads and microwave synthesizers used in this work are presented. The vapor cell standards are useful in our everyday lives for applications ranging from telecommunications, navigation, metrology etc. In view of improving the performances of the Rb cell standards, two different clock approaches were studied in detail: The first one is on use of vapor cells (1.4 cm3) whose inner walls are coated with anti-relaxation material. A first ever wall-coated cell clock was demonstrated with good short-term frequency stability. The medium- to long-term stability was found to be limited by the temperature coefficient (TC) of the coating material itself. This work gave the insight to important features to be considered in future anti-relaxation coating materials for atomic standards. The second novel approach involves using a bigger cell (12 cm3) within a newly developed, improved MWR towards a high-performance atomic standard. Adopting a larger cell gives a higher atomic Q-factor signal that improves the short-term clock stability. In this approach, the cell was filled with 87Rb and buffer gases. With this clock, we demonstrate the state-of-the-art short-term stability of <1.4×10−13 τ−1/2. Metrological quantitative measurements on parameters influencing the medium- to long-term stability were studied in view of next generation satellite navigation systems that demand a stability level of <1×10−14 at 10 4 s (equivalent to <1 ns/day). The potential of short-term stability and understanding of the limiting factors on medium- to long-term time scales demonstrated in this study pave the way for future work towards the commercialization of high-performance Rb atomic clocks for a variety of applications.
We report our investigations on a compact high-performance rubidium (Rb) vapourcell clock based on microwave-optical double-resonance (DR).These studies are done in both DR continuous-wave (CW) and Ramsey schemes using the same Physics Package (PP), with the same Rb vapour cell and a magnetron-type cavity with only 45 cm 3 external volume.In the CW-DR scheme, we demonstrate a DR signal with a contrast of 26% and a linewidth of 334 Hz; in Ramsey-DR mode Ramsey signals with higher contrast up to 35% and a linewidth of 160 Hz have been demonstrated.Short-term stabilities of 1.4×10 -13 τ -1/2 and 2.4×10 -13 τ -1/2 are measured for CW-DR and Ramsey-DR schemes, respectively.In the Ramsey-DR operation, thanks to the separation of light and microwave interactions in time, the light-shift effect has been suppressed which allows improving the long-term clock stability as compared to CW-DR operation.Implementations in miniature atomic clocks are considered. IntroductionSince the first invention of lamp-pumped rubidium (Rb) clocks in the 1960's [1,2], the demand for a stable, reliable, and compact Rb frequency standard with low power consumption has been growing, for various applications fields such as industry, telecommunication, navigation, space applications (e.g.GPS [3], GALILEO [4] and COMPASS [5]).Recently, thanks to the semiconductor laser technology, laser-pumped Rb clocks have been considered in several studies, for their better optical pumping efficiency results in short-term frequency stabilities at least one order of magnitude better than their lamp-pumped counterparts [6][7][8][9].This opened up also several new schemes for vapour-cell atomic clocks, such as the continuous-wave (CW) Rb clock [9], coherent population trapping (CPT) Cs clock [10] and pulsed optical pumping (POP) Rb clock [11].In this paper we report our studies on high-performance Rb frequency standards based on the laser-microwave double-resonance (DR) scheme, using both CW and Ramsey interrogation.Both CW-DR and Ramsey-DR schemes require two resonant electromagnetic fields of light and microwave.In the case of CW-DR, the laser optically pumps the vapour of the Rb atoms by creating a polarization of the atomic ground-state; simultaneously the microwave field, generated from a quartz oscillator and is near-resonant with the 87 Rb hyperfine clock transition (energy levels 5 2 S 1/2 │F g =1, m F =0˃ ↔│F g =2, m F =0˃), is applied.The opacity of the Rb vapour to the transmitted light signal as a function of microwave frequency is a measure of the atomic ground state polarization known as CW-DR signal [9].In CW-DR, the steps of optical pumping, microwave interrogation and optical detection are applied simultaneously (figure 1(b)).In the case of Ramsey-DR, these three sequences are separated in time, see figure 1(c): first, during optical pumping a strong laser pulse creates a significant atom population imbalance between
We present a prospective experimental study on double-resonance Ramsey spectroscopy in a micro fabricated Rb vapor cell, in view of future miniature atomic clocks with improved stability performance. Ramsey signals with a narrow central fringe width of 1.5 kHz combined with a competitive contrast of > 5 % are observed, resulting in a clock short-term stability of ≈ 1×10-11τ−1/2. The employed pulsed optical pumping (POP) scheme bears promise for reduced light-shift effects and thus for improved clock stability on medium- to long-term timescales.
We present a demonstration of a cold-atom optical-microwave double resonance (DR) Ramsey clock utilising an additively manufactured loop-gap-resonator cavity and grating magneto-optical trap (GMOT). The use of additive manufacturing allows for complex cavity structures, more difficult to produce with traditional machining techniques, while the GMOT architecture significantly simplifies the optical system required to trap and cool the atomic sample. In the current demonstration a single laser is used to trap < 3 × 106 87Rb atoms, cool them to below 10 µK, optically pump and read-out state populations of the atoms after microwave interrogation. A Ramsey-type interrogation scheme is employed with an empirically evaluated optimum free evolution time of 10 ms, limited by the loss of signal due to atoms falling out of the read-out beam. We demonstrate a short-term stability of < 2×10−11τ−1/2, in reasonable agreement with the predicted short-term stability based on the signal to noise ratio of the measured Ramsey fringes. Excellent field homogeneity of the cavity microwave field is demonstrated though Rabi oscillations, while almost complete optical pumping and good field orientation is evidenced by Zeeman spectroscopy of the ground-state hyperfine energy levels. This work is a novel approach towards more compact and portable cold-atom microwave clocks with significant potential for further miniaturization of the system.