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Optics Letters

Dependence of small-scale atomic clock performance on frequency modulation parameters used in the frequency control loop

Matan Kahanov, Ido Ben-Aroya, G. Eisenstein

Published Apr 23, 2008• 7 citations
Publisher

Abstract

We demonstrate a direct correspondence between FM parameters used in a frequency-locked loop that is based on multifield FM spectroscopy and the stability of a small-scale coherent population trapping atomic clock. Optimized FM parameters lead to an Allan deviation of 2.8 x 10(-11)/square root tau, while the clock stability deteriorates in a predictable manner for the other FM parameters.

DOI
10.1364/ol.33.000944

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We demonstrate a direct correspondence between FM parameters used in a frequency-locked loop that is based on multifield FM spectroscopy and the stability of a small-scale coherent population trapping atomic clock. Optimized FM parameters lead to an Allan deviation of 2.8 x 10(-11)/square root tau, while the clock stability deteriorates in a predictable manner for the other FM parameters.
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.
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.
This work reports for the first time development and experimental study of a laboratory prototype of an atomic clock with stability of 2×10–11τ –1/2 (Allan deviation) over time 1 s < τ < 1000 s (7×10–13 over 1000 s) on the basis of a coherent population trapping (CPT) resonance in 87Rb in a compact spherical cell having 1.3-cm diameter and without any buffer gas. Demonstrated are dependencies of the width of the studied CPT resonance upon the amplitude and modulation frequency of optical frequency difference (3.417 GHz) of a bichromatic circularly polarised pump field. For the first time, a considerable non-linearity was discovered in the dependence upon the reference difference frequency of the spectral position of the CPT resonance when the modulation frequency of the optical frequency difference is varied within a broad range.
Abstract Chip-scale atomic clocks based on coherent population trapping (CPT) face challenges due to miniaturized gas cells, which reduces the CPT resonance signal and the absorption signals of alkali atoms. To overcome this, we propose a method that simultaneously stabilizes the laser wavelength and microwave modulation frequency without relying on absorption line detection. Our approach enables stabilization at the point where the amplitude of the CPT resonance signal is maximized, making it suitable for compact atomic clocks. The system uses three lock-in amplifiers: one is used to stabilize the RF modulation frequency, and the other two are used for detecting the amplitude of the CPT resonance and stabilizing the laser wavelength. The Allan deviation measurements demonstrate a 1.4-fold improvement in short-term stability compared to conventional methods, suggesting that the proposed technique is a promising solution for enhancing the performance of small gas-cell atomic clocks.