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Applied Physics Letters

Mitigation of the magnetic-field-induced frequency shift in coherent-population-trapping atomic clocks

Denis V. Brazhnikov, V. I. Vishnyakov, Mikhail N Skvortsov

Published Dec 29, 2025• 1 citation
Publisher

Abstract

We study the magnetic-field-induced frequency shift (MFS) of the reference resonance in a coherent population trapping (CPT) microwave atomic clock. It is shown that the use of the Pound–Drever–Hall-like technique for frequency locking provides brilliant opportunities for mitigating the MFS. Using a 0.125 cm3 rubidium vapor cell with a buffer gas, we have measured a residual sensitivity of the reference CPT resonance frequency to be ≈70μHz/mG over ≈6 mG interval. It means that a fractional frequency shift is extremely small (≈1×10−14 mG−1). The results contribute to the development of a new-generation CPT-based miniature atomic clock with improved long-term frequency stability. The proposed method is sufficiently versatile and can be adapted for other excitation schemes in atomic clocks, including those based on Ramsey-like or double-resonance techniques.

DOI
10.1063/5.0305867

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Journal of the Optical Society of America B•Nov 1, 2006•23 citations
We study the magnetic-field-induced frequency shift (MFS) of the reference resonance in a coherent population trapping (CPT) microwave atomic clock. It is shown that the use of the Pound–Drever–Hall-like technique for frequency locking provides brilliant opportunities for mitigating the MFS. Using a 0.125 cm3 rubidium vapor cell with a buffer gas, we have measured a residual sensitivity of the reference CPT resonance frequency to be ≈70μHz/mG over ≈6 mG interval. It means that a fractional frequency shift is extremely small (≈1×10−14 mG−1). The results contribute to the development of a new-generation CPT-based miniature atomic clock with improved long-term frequency stability. The proposed method is sufficiently versatile and can be adapted for other excitation schemes in atomic clocks, including those based on Ramsey-like or double-resonance techniques.
We study the magnetic-field-induced frequency shift (MFS) of the clock (``0--0'') transition in coherent-population-trapping (CPT) microwave atomic clock. It is shown that the use of the Pound-Drever-Hall-like (PDH) technique for frequency locking provides brilliant opportunities for mitigating the MFS. Using a 0.1250.1250.125 cm3^33 rubidium vapor cell with a buffer gas, we have measured a residual sensitivity of the clock transition frequency to be ≈ 72\approx\,72≈72 μμμHz/mG over ≈ \approx\,≈666 mG interval. It means that a fractional frequency shift is extremely small (≈ \approx\,≈111 × \,\times\,×10−1410^{-14}10−14 mG−1^{-1}−1). The results contribute to the development of a new-generation CPT-based miniature atomic clock (MAC) with improved long-term frequency stability. The proposed method is quite general and can be used for other excitation schemes in atomic clocks, including Ramsey-like techniques.
We investigate the magnetic-field-induced frequency shift (MFS) of the clock “0–0” transition in the microwave quantum frequency standard (atomic clock) based on coherent population trapping (CPT) in 87Rb vapor. To scan the CPT resonance and to form the error signal, a method analogous to the Pound–Drever–Hall (PDH) technique in the optical frequency range is employed, where the modulating frequency (fm) significantly exceeds the resonance linewidth (FWHM). The experiments demonstrate that this technique offers brilliant capabilities for controlling the sensitivity of the clock transition frequency to magnetic field variations in the vapor cell compared to the conventional method with low-frequency modulation (fm≪FWHM). Specifically, the PDH technique provides several optimal values of the bias magnetic field generated by the solenoid, at which the “0–0” transition frequency exhibits extremely low sensitivity to small variations in the external magnetic field. Furthermore, these magnetic field values can be easily adjusted by changing fm, which is relevant for the optimization of the atomic clock’s operating regime. The experimental results show that by using the PDH technique, the influence of MFS on the clock transition can be suppressed down to ≈3.2×10−13δB2mG−2. These findings can be leveraged both to relax stringent requirements for magnetic field shielding in state-of-the-art CPT-based miniature atomic clocks and to build a new generation of such clocks with long-term frequency stability better than 10−12.
Abstract Chip-scale atomic clocks based on coherent population trapping (CPT) face challenges due to miniaturized gas cells, which reduces the CPT resonance signal and the absorption signals of alkali atoms. To overcome this, we propose a method that simultaneously stabilizes the laser wavelength and microwave modulation frequency without relying on absorption line detection. Our approach enables stabilization at the point where the amplitude of the CPT resonance signal is maximized, making it suitable for compact atomic clocks. The system uses three lock-in amplifiers: one is used to stabilize the RF modulation frequency, and the other two are used for detecting the amplitude of the CPT resonance and stabilizing the laser wavelength. The Allan deviation measurements demonstrate a 1.4-fold improvement in short-term stability compared to conventional methods, suggesting that the proposed technique is a promising solution for enhancing the performance of small gas-cell atomic clocks.
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 ($\ensuremath{\lambda}\ensuremath{\approx}895$ 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.
We report on measurements of frequency shifts in a microwave cesium vapor cell atomic clock based on coherent population trapping (CPT). The dependence of the clock frequency on numerous experimental parameters, such as the laser power, the laser frequency, the microwave power, the cell temperature, the static magnetic field, but also the temperature of some key components, or the translation and rotation of critical wave plates and optical elements, is investigated. The stability budget of the clock frequency at one day is reported and discussed. This study constitutes a solid database for the future demonstration of a CPT-based cell clock with enhanced mid- and long-term stability performances.
We present a microwave frequency standard based on coherent population trapping (CPT) in the 87Rb D1 line. The CPT spectrum is obtained using two Raman lasers with a 6.8 GHz frequency offset by injection locking of a master laser to a slave laser. We have constructed an atomic clock employing a 5 cm long Rb vapor cell confined with 6.67 kPa neon buffer gas at 70 °C. Using this system, we improve the CPT contrast through the elimination of undesired off-resonant fields created by the direct modulation method. We measured the frequency shift of the CPT signal as a function of the temperature of the Rb cell and estimated it to be approximately 1.3 ×10−9/K. The frequency of a 10 MHz crystal oscillator has been stabilized to the CPT spectrum between the two ground states in 87Rb. The relative frequency stability is approximately 2.3×10−12 for an average time of 68 s.