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

Improving the frequency stability of atomic frequency standard basing on the noise asynchromism correction

Qian Wang, Rong Wei, Richang Dong, Jinda Lin, Wenli Wang, Yuzhu Wang

Published Jul 1, 2017• 0 citations
Publisher

Abstract

We propose an improvement for increasing the performance of locked periodic atomic frequency standards(AFS), based on correcting the noise of the asynchronism of phase-detecting and feedback process. Theoretical analysis and numerical simulation show that the method can optimize the stability AFS which is related with d. And is the duty of phase-discriminating of AFS. If in-loop noise possesses white frequency noise characteristics, the stability will decrease following the coefficient of √(1 − d). Specially, when d approaches to 1, the stability will reach the limit of quantum project noise. Here we demonstrate three schemes to realize the idea in experiments and overlap-feedback is the most easily implemented one. Considering Dick effect in our method, the stability of our atomic fountain will be better than 1 × 10−14τ−1/2at d>0.93.

DOI
10.1109/fcs.2017.8088864

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We propose an improvement for increasing the performance of locked periodic atomic frequency standards(AFS), based on correcting the noise of the asynchronism of phase-detecting and feedback process. Theoretical analysis and numerical simulation show that the method can optimize the stability AFS which is related with d. And is the duty of phase-discriminating of AFS. If in-loop noise possesses white frequency noise characteristics, the stability will decrease following the coefficient of √(1 − d). Specially, when d approaches to 1, the stability will reach the limit of quantum project noise. Here we demonstrate three schemes to realize the idea in experiments and overlap-feedback is the most easily implemented one. Considering Dick effect in our method, the stability of our atomic fountain will be better than 1 × 10−14τ−1/2at d>0.93.
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 introduce concepts from optimal estimation to the stabilization of precision frequency standards limited by noisy local oscillators. We develop a theoretical framework casting various measures for frequency standard variance in terms of frequency-domain transfer functions, capturing the effects of feedback stabilization via a time series of Ramsey measurements. Using this framework, we introduce an optimized hybrid predictive feedforward measurement protocol that employs results from multiple past measurements and transfer-function-based calculations of measurement covariance to improve the accuracy of corrections within the feedback loop. In the presence of common non-Markovian noise processes these measurements will be correlated in a calculable manner, providing a means to capture the stochastic evolution of the local oscillator frequency during the measurement cycle. We present analytic calculations and numerical simulations of oscillator performance under competing feedback schemes and demonstrate benefits in both correction accuracy and long-term oscillator stability using hybrid feedforward. Simulations verify that in the presence of uncompensated dead time and noise with significant spectral weight near the inverse cycle time predictive feedforward outperforms traditional feedback, providing a path towards developing a class of stabilization software routines for frequency standards limited by noisy local oscillators.
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.
Atomic clocks have reached the Quantum Projection Noise (QPN) limit of stability and it has been proposed to use the entangled atomic ensemble in order to overcome the QPN limit. We have proposed a new method to lock the phase of the Local Oscillator (LO) to the atomic phase and call, "atomic phase lock (APL)." This APL could possibly overcome the QPN limit without need of preparing the entangled atomic ensemble. Traditional Ramsey method destroys the coherence of the atomic spin due to the projection measurement at each cycle. This destruction and initialization of the phase at each cycle introduce additional noise and the performance of the atomic clock is limited at the white frequency noise level. APL employs dispersion measurements, i.e. Faraday rotation, in order to measure the phase difference without destroying the atomic phase. By repeating the measurement cycle with sufficiently small dead time, one can suppress the LO noise down to white phase noise level, achieving the τ-1 dependence of the Allan variance that can eventually overcome the QPN limit in long term. We are preparing a proof-of-principle experiment using the ensemble of trapped 171Yb+ ions with hyperfine splitting (12.6 GHz) as a clock transition and report the current status of the experiment as well.
We propose a new method to reduce the frequency noise of a Local Oscillator (LO) to the level of white phase noise by maintaining (not destroying by projective measurement) the coherence of the ensemble pseudo-spin of atoms over many measurement cycles. This scheme uses weak measurement to monitor the phase in Ramsey method and repeat the cycle without initialization of phase and we call, "atomic phase lock (APL)" in this paper. APL will achieve white phase noise as long as the noise accumulated during dead time and the decoherence are smaller than the measurement noise. A numerical simulation confirms that with APL, Allan deviation is averaged down at a maximum rate that is proportional to the inverse of total measurement time, tau^-1. In contrast, the current atomic clocks that use projection measurement suppress the noise only down to the level of white frequency, in which case Allan deviation scales as tau^-1/2. Faraday rotation is one of the possible ways to realize weak measurement for APL. We evaluate the strength of Faraday rotation with 171Yb+ ions trapped in a linear rf-trap and discuss the performance of APL. The main source of the decoherence is a spontaneous emission induced by the probe beam for Faraday rotation measurement. One can repeat the Faraday rotation measurement until the decoherence become comparable to the SNR of measurement. We estimate this number of cycles to be ~100 cycles for a realistic experimental parameter.