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arXiv:2411.03190

Frequency locking: a distinctive feature of the coherent population trapping and the stationarity effect

Eugene A. Tsygankov, Dmitry S. Chuchelov, Maria I. Vaskovskaya, Vitali V. Vassiliev, Sergei A. Zibrov, Vladimir L Velichansky

Published Nov 5, 2024• 0 citations
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Abstract

We study the case where phase modulation of the harmonic signal is used to obtain the error signal for the frequency stabilization to a reference atomic transition. High-frequency modulation, or analog of the Pound-Drever-Hall regime, is considered. We demonstrate that for coherent population trapping, the maximal error-signal slope retains at a certain level with growth in the modulation frequency, while for other types of resonances it drops steadily. The investigation of the low-frequency modulation regime reveals the stationarity effect. We show that in this case, the maximal steepness of the error signal does not depend on the modulation frequency and is reached at a fixed value of the frequency deviation.

DOI
10.48550/arxiv.2411.03190

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We investigate the use of phase modulation to generate an error signal for frequency stabilization to a reference atomic transition. The study focuses on the high-frequency modulation regime. Our theoretical analysis shows that, in the case of coherent population trapping, the maximal slope of the error signal remains constant as the modulation frequency increases, whereas it steadily decreases for other types of resonances. Experimental results with 87Rb atoms confirm this behavior under comparison with the double radio-optical resonance.
We theoretically investigate the dynamic regime of coherent population trapping (CPT) in the presence of frequency modulation (FM). We have formulated the criteria for quasi-stationary (adiabatic) and dynamic (non-adiabatic) responses of atomic system driven by this FM. Using the density matrix formalism for Λ system, the error signal is exactly calculated and optimized. It is shown that the optimal FM parameters correspond to the dynamic regime of atomic-field interaction, which significantly differs from conventional description of CPT resonances in the frame of quasi-stationary approach (under small modulation frequency). Obtained theoretical results are in good qualitative agreement with different experiments. Also we have found CPT-analogue of Pound-Driver-Hall regime of frequency stabilization.
We study the coherent population trapping resonance induced by the radiation of a microwave-current-modulated diode laser. The situation is considered when a harmonic phase modulation of the microwave field is used to generate the error signal for the frequency stabilization of atomic clocks. We demonstrate that in this case the resonance acquires a multipeak structure. If it is asymmetric and the components of the multipeak structure are not fully resolved, then the resonance frequency nonlinearly depends on the laser field intensity. The peaks become separated at an increase in the frequency of the phase modulation, providing a linear dependence of the frequency on the intensity of the laser field. This theoretical prediction is confirmed experimentally. Other advantages of the high-frequency modulation regime are also discussed.
The appearance of the population difference in the ground state of the Λ\Lambda Λ -system due to the spontaneous decay of the upper level into lower ones is considered. The resulting asymmetry of the coherent population trapping resonance is shown to lead to a frequency shift of the quadrature signal, which nonlinearly depends on the optical field intensity. In this case, this contribution is not suppressed due to the use of high modulation frequencies compared to the relaxation rate of ground state polarization (analogue of the Pound–Drever–Hall technique). A significant smallness of this shift when using a binary mixture of noble buffer gases is discussed.
We theoretically study the frequency shift in atomic clocks caused by the line-shape asymmetry of coherent population trapping (CPT) resonance in a bichromatic laser field. This asymmetry arises due to the inequality of the resonant spectral components and nonzero one-photon detuning. The line-shape-asymmetry-induced shift depends on the intensity of the resonant fields, which leads to a degradation in long-term stability due to fluctuations of the laser field parameters. A frequency stabilization based on the harmonic modulation of two-photon detuning is considered. It is shown that the use of a high-frequency modulation (compared to the CPT resonance width, i.e., the Pound-Drever-Hall regime) makes it possible to significantly suppress this shift (by one to two orders of magnitude).