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arXiv:2311.00461 · Physical Review Applied

Light shift mitigation in microcell-based coherent-population-trapping atomic clocks in the field of two circularly polarized light beams

Denis V. Brazhnikov, S M Ignatovich, Mikhail N Skvortsov

Published May 23, 2024• 8 citations
arXivHTMLPDF

Abstract

State-of-the-art miniature atomic clocks (MACs) are based on the phenomenon of coherent population trapping (CPT) in alkali-metal atomic vapors ($\mathrm{Rb}$ or $\mathrm{Cs}$). Improving the stability of the clock frequency is a crucial issue; resolving it would result in significant progress in numerous applications. Here, we examine the configuration of the light field, which is composed of two bichromatic beams with opposing handedness of circular polarization. The beams are in resonance with optical transitions in the $\mathrm{Cs}$ ${D}_{1}$ line ($\ensuremath{\lambda}\ensuremath{\approx}895$ nm). This configuration has previously been shown to produce observed CPT resonances with higher contrast than a standard single-beam scheme; however, our scheme implements pump and probe beams that operate independently, with the transmission of the probe beam being monitored separately. This approach differs from previous studies. The experiments are carried out using a cubic $5\ifmmode\times\else\texttimes\fi{}5\ifmmode\times\else\texttimes\fi{}5\phantom{\rule{0.2em}{0ex}}{\mathrm{mm}}^{3}$ vapor cell filled with buffer gas. It is shown that the line shape of the resonance acquires an asymmetry that can be efficiently controlled by a microwave (Raman) phase between the beams. As a proof of concept, we study the way in which this asymmetry can help to mitigate the influence of the ac Stark (light) shift on the long-term frequency stability of CPT clocks based on vapor microcells ($V\ensuremath{\ll}1\phantom{\rule{0.2em}{0ex}}{\mathrm{cm}}^{3}$). Experimental verification is performed with both a distributed-Bragg-reflector laser and a vertical-cavity surface-emitting laser. The latter is of particular importance for the development of MACs. The experimental results are in qualitative agreement with the analytical theory based on a double-$\mathrm{\ensuremath{\Lambda}}$ scheme of atomic energy levels.

DOI
10.1103/physrevapplied.21.054046

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State-of-the-art miniature atomic clocks (MACs) are based on the phenomenon of coherent population trapping (CPT) in alkali-metal atomic vapors (Rb\mathrm{Rb}Rb or Cs\mathrm{Cs}Cs). Improving the stability of the clock frequency is a crucial issue; resolving it would result in significant progress in numerous applications. Here, we examine the configuration of the light field, which is composed of two bichromatic beams with opposing handedness of circular polarization. The beams are in resonance with optical transitions in the Cs\mathrm{Cs}Cs D1{D}_{1}D1​ line (\ensuremathλ\ensuremath≈895\ensuremath{\lambda}\ensuremath{\approx}895\ensuremathλ\ensuremath≈895 nm). This configuration has previously been shown to produce observed CPT resonances with higher contrast than a standard single-beam scheme; however, our scheme implements pump and probe beams that operate independently, with the transmission of the probe beam being monitored separately. This approach differs from previous studies. The experiments are carried out using a cubic 5\ifmmode×\else\texttimes\fi5\ifmmode×\else\texttimes\fi5mm35\ifmmode\times\else\texttimes\fi{}5\ifmmode\times\else\texttimes\fi{}5\phantom{\rule{0.2em}{0ex}}{\mathrm{mm}}^{3}5\ifmmode×\else\texttimes\fi5\ifmmode×\else\texttimes\fi5mm3 vapor cell filled with buffer gas. It is shown that the line shape of the resonance acquires an asymmetry that can be efficiently controlled by a microwave (Raman) phase between the beams. As a proof of concept, we study the way in which this asymmetry can help to mitigate the influence of the ac Stark (light) shift on the long-term frequency stability of CPT clocks based on vapor microcells (V\ensuremath≪1cm3V\ensuremath{\ll}1\phantom{\rule{0.2em}{0ex}}{\mathrm{cm}}^{3}V\ensuremath≪1cm3). Experimental verification is performed with both a distributed-Bragg-reflector laser and a vertical-cavity surface-emitting laser. The latter is of particular importance for the development of MACs. The experimental results are in qualitative agreement with the analytical theory based on a double-\ensuremathΛ\mathrm{\ensuremath{\Lambda}}\ensuremathΛ scheme of atomic energy levels.
We report the characterization of dark line resonances observed in Cs vapor microcells filled with a unique neon (Ne) buffer gas. The impact on the coherent population trapping (CPT) resonance of some critical external parameters such as laser intensity, cell temperature, and microwave power is studied. We show the suppression of the first-order light shift by proper choice of the microwave power. The temperature dependence of the Cs ground state hyperfine resonance frequency is shown to be canceled in the 77–80 °C range for various Ne buffer gas pressures. The necessity to adjust the Ne buffer gas pressure or the cell dimensions to optimize the CPT signal height at the frequency inversion temperature is pointed out. Based on such Cs–Ne microcells, we preliminary demonstrate a 852 nm vertical cavity surface emitted laser (VCSEL)-modulated based CPT atomic clock exhibiting a short term fractional frequency instability σy(τ)=1.5×10−10τ−1/2 until 30 s. These results, similar to those published in the literature by others groups, prove the potential of our original microcell technology in view of the development of high-performance chip scale atomic clocks.
Light shifts are known to be an important limitation to the mid- and long-term fractional frequency stability of different types of atomic clocks. In this article, we demonstrate the experimental implementation of an anti-light-shift interrogation protocol onto a continuous-wave (cw) microcell atomic clock based on coherent population trapping (CPT). The method, inspired by the autobalanced Ramsey spectroscopy technique demonstrated in pulsed atomic clocks, consists in the extraction of atomic based information from two successive light-shifted clock frequencies obtained at two different laser-power values. Two error signals, computed from the linear combination of signals acquired along a symmetric sequence, are managed in a dual-loop configuration to generate a clock frequency free from light shift. Using this method, the sensitivity of the clock frequency to both laser-power and microwave-power variations can be reduced by more than an order of magnitude compared to normal operation. In the present experiment, the consideration of the nonlinear light-shift dependence allows enhancement of the light-shift mitigation. The implemented technique allows an improvement of the clock Allan deviation for time scales higher than 1000 s. This method can be applied in various kinds of atomic clocks such as CPT-based atomic clocks, double-resonance Rb\mathrm{Rb}Rb clocks, or cell-stabilized lasers.
In this study, the Ramsey spectroscopy of coherent population trapping resonances excited on the D1 line of alkali metal atoms in miniature vapor cells has been studied theoretically and experimentally. The configuration of the field produced by two counterpropagating waves with opposite circular polarizations has been considered. A counterpropagating wave is formed as a result of reflection from a partially transmitting output mirror, while the signal from the initial wave transmitted through the mirror is detected. It is shown that such a scheme is characterized by the optimal mirror reflection coefficient, for which the short-term stability can be substantially improved relative to the standard scheme without the counterpropagating wave. The three-fold improvement of the short-term stability of the atomic clock based on the coherent population trapping resonance in a vapor cell with 87Rb atoms has been demonstrated experimentally.
We present a joint theoretical and experimental characterization of the coherent population trapping (CPT) resonance excited on the D1{D}_{1}D1​ line of 87Rb^{87}\mathrm{Rb}87Rb atoms by bichromatic linearly polarized laser light. We observe high-contrast transmission resonances (up to $\ensuremath{\approx}25%$), which makes this excitation scheme promising for miniature all-optical atomic clock applications. We also demonstrate cancellation of the first-order light shift by proper choice of the frequencies and relative intensities of the two laser-field components. Our theoretical predictions are in good agreement with the experimental results.
Vapor cell atomic clocks exhibit reduced frequency stability for averaging time between about one hundred and a few thousand seconds. Here we report a study on the impact of the main parameters on the mid-to-long term instability of a buffer-gas vapor cell Cs clock, based on coherent population trapping (CPT). The CPT signal is observed on the Cs D1 line transmission, using a double Λ scheme and a Ramsey interrogation technique. The effects on the clock frequency of the magnetic field, the cell temperature, and the laser intensities are reported. We show in particular that the laser intensity shift is temperature dependent. Along with the laser intensity ratio and laser polarization properties, this is one of the most important parameters.
We report on the performance of the first table-top prototype atomic clock based on coherent population trapping (CPT) resonances with parallel linearly polarized optical fields (lin‖lin configuration). Our apparatus uses a vertical-cavity surface-emitting laser (VCSEL) tuned to the D1 line of 87Rb with the current modulation at the 87Rb hyperfine frequency. We demonstrate cancellation of the first-order light shift by the proper choice of rf modulation power and further improve our prototype clock stability by optimizing the parameters of the microwave lock loop. Operating in these optimal conditions, we measured a short-term fractional frequency stability (Allan deviation) 2×10−11τ−1/2 for observation times 1 s ≤ τ ≤ 20 s. This value is limited by large VCSEL phase noise and environmental temperature fluctuation. Further improvements in frequency stability should be possible with an apparatus designed as a dedicated lin‖lin CPT resonance clock with environmental impacts minimized.