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Optics Express

Dynamic regime of coherent population trapping and optimization of frequency modulation parameters in atomic clocks

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

Published Feb 2, 2017• 29 citations
Publisher

Abstract

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.

DOI
10.1364/oe.25.002742

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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.
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 describe the optimization of a Frequency Locked Loop (FLL) in an atomic clock which is based on Coherent Population Trapping (CPT) in (87)Rb vapor using the D(2) transition. The FLL uses frequency modulation (FM) spectroscopy and we study the effect of FM parameters (modulation frequency and index) on the sensitivity and the signal to noise ratio of the feedback signal in the FLL. The clock which employs a small spherical glass cell containing (87)Rb atoms and a buffer gas, exhibits a short term stability of 3x10(-11)/ radicaltau. The long term relative frequency stability of the 10 MHz output is better than 10(-10) with a drift of 10(-11) per day.
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.
Coherent population trapping (CPT) resonance formation is modeled numerically in a three-level Λ -system with one of the near-resonance fields being frequency-modulated. The model is based on density matrix equations in RW approximation with atomic relaxation properly taken into account. Slow modulation is shown to be equivalent to CW excitation with the frequency changed point by point. As the modulation period approaches the relaxation times, the delayed response of the system is shown to cause the CPT resonance shift and reshaping, as well as the appearance of transient oscillations of the energy level populations.