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arXiv:1911.00575 · Physical Review Applied

Dynamic Continuous-Wave Spectroscopy of Coherent Population Trapping at Phase-Jump Modulation

M. Yu. Basalaev, V.I. Yudin, A.V. Taichenachev, M.I. Vaskovskaya, D.S. Chuchelov, S.A. Zibrov, V.V. Vassiliev, Vladimir L Velichansky

Published Mar 24, 2020• 17 citations

Abstract

A method of dynamic continuous-wave spectroscopy of coherent population trapping (CPT) resonances using phase modulation of the jump type is developed. The time evolution of the spectroscopic signal is investigated. A method for the formation of an error signal for frequency stabilization is proposed. We show that our approach has a reduced sensitivity to the line-shape asymmetry of the CPT resonance. The experimental results are in good qualitative agreement with theoretical predictions based on a mathematical model of a three-level $\mathrm{\ensuremath{\Lambda}}$ system in a bichromatic field. This method can be used in atomic frequency standards (including chip-scale atomic clocks).

DOI: 10.1103/physrevapplied.13.034060

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A method of dynamic continuous-wave spectroscopy of coherent population trapping (CPT) resonances using phase modulation of the jump type is developed. The time evolution of the spectroscopic signal is investigated. A method for the formation of an error signal for frequency stabilization is proposed. We show that our approach has a reduced sensitivity to the line-shape asymmetry of the CPT resonance. The experimental results are in good qualitative agreement with theoretical predictions based on a mathematical model of a three-level

\mathrm{\ensuremath{\Lambda}}

system in a bichromatic field. This method can be used in atomic frequency standards (including chip-scale atomic clocks).

We present the research of dynamic continuous-wave spectroscopy of the coherent population trapping resonance at the phase-jump modulation. Λ system of levels supplemented by a nonabsorbing state and bichromatic optical field, whose spectral components have different intensities, are considered. We demonstrate that the asymmetry leads to an additional nonlinear shift of the error-signal frequency under unisotropic relaxation of the ground-state density-matrix elements. We also investigate the conventional approach where the frequency difference of the optical field components is harmonically modulated to obtain the error signal. Comparison demonstrates that in the high-frequency modulation regime the corresponding frequency shift is more linear than at the phase-jump modulation for nonshort integration times.

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.

Motivated by recent developments in atomic frequency standards employing the effect of coherent population trapping (CPT), we propose a theoretical framework for the frequency modulation spectroscopy of the CPT resonances. Under realistic assumptions we provide simple yet non-trivial analytical formulae for the major spectroscopic signals such as the CPT resonance line and the in-phase/quadrature responses. We discuss the influence of the light shift and, in particular, derive a simple expression for the displacement of the resonance as a function of modulation index. The performance of the model is checked against numerical simulations, the agreement is good to perfect. The obtained results can be used in more general models accounting for light absorption in the thick optical medium.