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arXiv:2502.11587 · Journal of Applied Physics

Reduction of magnetic-field-induced shift in quantum frequency standards based on coherent population trapping

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

Published Apr 25, 2025• 6 citations

Abstract

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.

DOI: 10.1063/5.0265574

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Journal of the Optical Society of America B•Nov 1, 2006•23 citations

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.

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

0.125

cm

^3

rubidium vapor cell with a buffer gas, we have measured a residual sensitivity of the clock transition frequency to be

\approx\,72

μ

Hz/mG over

\approx\,

6

mG interval. It means that a fractional frequency shift is extremely small (

\approx\,

1

\,\times\,

10^{-14}

mG

^{-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 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.

The active suppression of light shift of the reference coherent population trapping (CPT) resonance in 87Rb vapor to improve the long-term stability of compact atomic clocks has been demonstrated experimentally. The approach is based on the phase jump technique used to synthesize an error signal, which is proportional to the light shift of the CPT resonance, from an optical transmission signal. The use of this error signal in an additional feedback loop allows one to stabilize the amplitude of a microwave signal for the phase modulation of laser radiation near a value at which the light shift of the CPT resonance is absent. This technique has made it possible to reduce the long-term instability of CPT atomic clocks in our experiments by a factor of 15 at an integration time of 10 000–20 000 s.

The active suppression of light shift of the reference coherent population trapping (CPT) resonance in87Rb vapor to improve the long-term stability of compact atomic clocks has been demonstrated experimentally. The approach is based on the phase jump technique used to synthesize an error signal, which is proportional to the light shift of the CPT resonance, from an optical transmission signal. The use of this error signal in an additional feedback loop allows one to stabilize the amplitude of a microwave signal for the phase modulation of laser radiation near a value at which the light shift of the CPT resonance is absent. This technique has made it possible to reduce the long-term instability of CPT atomic clocks in our experiments by a factor of 15 at an integration time of 10 000–20 000 s.

The authors demonstrate a simple technique to significantly improve the long-term frequency stability of atomic clocks based on coherent population trapping (CPT). In this technique, the CPT fields are created by a modulated diode laser and a slow servo is used to actively tune the laser modulation index to a value where the light shift vanishes. The observed clock frequency at this modulation index is given by the rubidium hyperfine frequency when no light fields are present, and this makes the clock frequency largely insensitive to variations in laser properties. In addition to reducing stringent requirements on the long-term stabilities of laser temperature, laser frequency, and rf modulation power, this technique may also significantly reduce frequency drifts related to laser aging. In the experiment, they demonstrate improvement by over one order of magnitude in the stability of a clock that is limited by light-shift-induced frequency drifts.

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.