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arXiv:1406.6673 · IEEE Transactions on Ultrasonics Ferroelectrics and Frequency Control

Dick effect in a pulsed atomic clock using coherent population trapping

Jean-Marie Danet, M. Lours, Stéphane Guérandel, Emeric de Clercq

Published Apr 1, 2014• 63 citations

Abstract

The Dick effect can be a limitation of the achievable frequency stability of a passive atomic frequency standard when the ancillary frequency source is only periodically sampled. Here, we analyze the Dick effect for a pulsed vapor cell clock using coherent population trapping (CPT). Because of its specific interrogation process without atomic preparation nor detection outside of the Ramsey pulses, it exhibits an original shape of the sensitivity function to phase noise of the oscillator. Numerical calculations using a three-level atom model are successfully compared with measurements; an approximate formula of the sensitivity function is given as an easy-to-use tool. A comparison of our CPT clock sensitivity to phase noise with a clock of the same duty cycle using a two-level system reveals a higher sensitivity in the CPT case. The influence of a free-evolution time variation and of a detection duration lengthening on this sensitivity is studied. Finally, this study permitted the choice of an adapted quartz oscillator and allowed an improvement of the clock fractional frequency stability at the level of 3.2 x 10-13at 1 s.

DOI: 10.1109/tuffc.2014.2945

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For most pulsed atomic clocks, the Dick effect is one of the main limits to reach its frequency stability limitation due to quantum projection noise. In this paper, we measure the phase noise of the local oscillator in the Ramsey-CPT atomic clock and calculate the Dick effect induced Allan deviation based on a three-level atomic model, which is quite different from typical atomic clocks. We further present a detailed analysis of optimizing the sensitivity function and minimizing the Dick effect by interleaving lock. By optimizing the duty circle of laser pulses, average time during detection and optical intensity of laser beam, the Dick effect induced Allan deviation can be reduced to the level of .

We propose a two-step pulse observation method to enhance the frequency stability of coherent population trapping (CPT) atomic clocks. The proposed method is a Raman–Ramsey scheme with low light intensity at resonance observation and provides a Ramsey-CPT resonance with both reduced frequency sensitivity to the light intensity and a high signal-to-noise ratio by reducing the repumping into a steady dark state. The resonance characteristics were calculated using density matrix analysis of a Λ-type three-level system that was modeled on the 133 Cs D 1 line, and the characteristics were also measured using a vertical-cavity surface-emitting laser and a Cs vapor cell.

A compact cold-atom clock based on coherent population trapping (CPT) has been developed. The clock typically demonstrates a short-term fractional frequency stability of 4×10−11/√τ, limited by frequency noise on the interrogation lasers. The clock interrogates a sample of 2×105atoms under free-fall with typical cycle and Ramsey periods of 50 ms and 16 ms, respectively. The largest two systematic frequency shifts that can limit the clock's long-term stability are the light shift and the Doppler shift.

We demonstrate a high-performance coherent-population-trapping (CPT) Cs vapor cell atomic clock using the push-pull optical pumping technique in the pulsed regime, allowing the detection of high-contrast and narrow Ramsey-CPT fringes. The impact of several experimental parameters onto the clock resonance and short-term fractional frequency stability, including the laser power, the cell temperature, and the Ramsey sequence parameters, has been investigated. We observe and explain the existence of a slight dependence on laser power of the central Ramsey-CPT fringe line-width in the pulsed regime. We report also that the central fringe line-width is commonly narrower than the expected Ramsey line-width given by 1/(2TR), with TR the free-evolution time, for short values of TR. The clock demonstrates a short-term fractional frequency stability at the level of 2.3×10−13 τ−1/2 up to 100 s averaging time, mainly limited by the laser amplitude modulation noise. Comparable performances are obtained in the conventional continuous wave regime, with the use of an additional laser power stabilization setup. The pulsed interaction allows to reduce significantly the clock frequency sensitivity to laser power variations, especially for high values of TR. This pulsed CPT clock, ranking among the best microwave vapor cell atomic frequency standards, could find applications in telecommunication, instrumentation, defense or satellite-based navigation systems.