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Joint Conference of the European Frequency and Time Forum and IEEE International Frequency Control Symposium (EFTF/IFCS)

Optimization of frequency modulation parameters in atomic clocks based on coherent population trapping

Valeriy I. Yudin, M. Yu. Basalaev, Д. В. Коваленко, А. В. Тайченачев

Published Jul 1, 2017• 0 citations
Publisher

Abstract

Excitation of coherent population trapping resonances in dynamic regime is theoretically investigated. We formulate the criteria for quasistationary (adiabatic) and dynamic (non-adiabatic) responses of atomic system driven by bichromatic field. We optimize the parameters of frequency modulation of two-photon detuning, taking into account the low-frequency noise.

DOI
10.1109/fcs.2017.8088877

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Excitation of coherent population trapping resonances in dynamic regime is theoretically investigated. We formulate the criteria for quasistationary (adiabatic) and dynamic (non-adiabatic) responses of atomic system driven by bichromatic field. We optimize the parameters of frequency modulation of two-photon detuning, taking into account the low-frequency noise.
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 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).
Abstract We develop a theory of modulation response of the coherent population trapping (CPT) resonance. We consider the simplest three-level atom, but take into account the polychromatic spectrum of the pumping and probing light produced by pure FM modulation of single frequency field. The analysis based on the density matrix equations rigorously includes the most important for applications range of modulation parameters where modulation frequency and deviation are comparable with or greater than the CPT linewidth, so the response of the atomic medium is not adiabatic. Some theoretical results, in particular the possibility of using a quadrature response to modulation to suppress light shift, are compared with the experiment carried out with a diode laser (VCSEL) and 87 Rb atoms.
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).