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Optics Express

Optimization of FM spectroscopy parameters for a frequency locking loop in small scale CPT based atomic clocks

Ido Ben-Aroya, Matan Kahanov, G. Eisenstein

Published Jan 1, 2007• 18 citations
Publisher

Abstract

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.

DOI
10.1364/oe.15.015060

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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.

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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 present a microwave frequency standard based on coherent population trapping (CPT) in the 87Rb D1 line. The CPT spectrum is obtained using two Raman lasers with a 6.8 GHz frequency offset by injection locking of a master laser to a slave laser. We have constructed an atomic clock employing a 5 cm long Rb vapor cell confined with 6.67 kPa neon buffer gas at 70 °C. Using this system, we improve the CPT contrast through the elimination of undesired off-resonant fields created by the direct modulation method. We measured the frequency shift of the CPT signal as a function of the temperature of the Rb cell and estimated it to be approximately 1.3 ×10−9/K. The frequency of a 10 MHz crystal oscillator has been stabilized to the CPT spectrum between the two ground states in 87Rb. The relative frequency stability is approximately 2.3×10−12 for an average time of 68 s.
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.
An atomic clock system based on coherent population trapping (CPT) resonance in 85 Rb is reported, while most past works about the CPT clock are in 87 Rb. A new modulation method (full-hyperfine-frequency-splitting modulation) is presented to reduce the effect of light shift to improve the frequency stability of the CPT clock in 85 Rb. The experimental results show that the short-term frequency stability of the CPT clock in 85 Rb is in the order of 10 −10 /s and the long-term frequency stability can achieve 1.5 × 10 −11 /80000 s, which performs as well as 87 Rb in CPT resonance. This very good frequency stability performance associated with the low-cost and low-power properties of 85 Rb indicates that an atomic clock based on CPT in 85 Rb should be a promising candidate for making the chip scale atomic clock.
We propose a novel way of radiation wavelength stabilisation in atomic clocks based on coherent population trapping (CPT). It uses quadrature-phase component of the CPT signal within the CPT resonance feedback loop and automatic wavelength locking of radiation from a VCSEL to the atomic absorption line. We demonstrate advantages and limitations of the new method applied to vapour cells with buffer gas or anti-relaxation coating. Also provided are measurements of short- and long-term stability of a CPT-based atomic clock using the proposed method with various optical cells. Discussed are the prospects of this method in chip-scale atomic clocks.
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.