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Chinese Physics Letters

An Accurate Frequency Control Method and Atomic Clock Based on Coherent Population Beating Phenomenon

Yu-Xin Zhuang, Daiting Shi, Dawei Li, Yigen Wang, Xiao-Na Zhao, Jianye Zhao, Zhong Wang

Published Apr 1, 2016• 7 citations
Publisher

Abstract

An accurate frequency control method and atomic clock based on the coherent population beating (CPB) phenomenon is implemented. In this scheme, the frequency difference of an rf and an atomic transition frequency can be digitally obtained by measuring the CPB oscillation frequency. The frequency measurement resolution of several milli-hertz can be achieved by using a 10 MHz oven controlled crystal oscillator as the reference. The expression of the Allan deviation of the CPB clock is theoretically deduced and it is revealed that the Allan deviation is inversely proportional to the signal-to-noise ratio and proportional to the line-width of coherent population trapping spectrum. We also approve that the CPB atomic clock has a large toleration of the drift of the local oscillator. In our CPB experimental system, a frequency instability of 3.0 × 10 −12 at 1000s is observed. The important feature of high frequency measurement resolution of the CPB method may also be used in magnetometers, atomic spectroscopy, and other related research.

DOI
10.1088/0256-307x/33/4/040601

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An accurate frequency control method and atomic clock based on the coherent population beating (CPB) phenomenon is implemented. In this scheme, the frequency difference of an rf and an atomic transition frequency can be digitally obtained by measuring the CPB oscillation frequency. The frequency measurement resolution of several milli-hertz can be achieved by using a 10 MHz oven controlled crystal oscillator as the reference. The expression of the Allan deviation of the CPB clock is theoretically deduced and it is revealed that the Allan deviation is inversely proportional to the signal-to-noise ratio and proportional to the line-width of coherent population trapping spectrum. We also approve that the CPB atomic clock has a large toleration of the drift of the local oscillator. In our CPB experimental system, a frequency instability of 3.0 × 10 −12 at 1000s is observed. The important feature of high frequency measurement resolution of the CPB method may also be used in magnetometers, atomic spectroscopy, and other related research.
We demonstrated an atomic clock based on coherent population beating (CPB). CPB occurs in typical Λ system, which enables us to obtain the beat frequency of the radio frequency for laser modulation and the hyperfine splitting. The beat frequency and its fluctuation is detected and accurately measured through digitized processing for compensating the shift of the radio frequency. It enables us to achieve a standard frequency which directly reference to the hyperfine transition. In our preliminary experiment an Allan Deviation of 3e-12 at 1000s is observed. CPB atomic clock eliminates the phase locking loop, and can be easily digitized and integrated.
We demonstrate a synchronously stimulation method for achieving coherent population beating (CPB) atomic clock with the CPB signal which have continuous wave and higher signal-to-noise ratio. In this method we synchronously apply the coherent population trapping (CPT) resonant stimulating lights together with the detuned detecting lights to obtain continuous CPB oscillation signal. Under the stimulation, the ground state coherence is maintained and the problem of CPB signal decaying is solved, which is beneficial for the measurement accuracy of the CPB frequency and the stability of the clock. The table experimental system of the synchronously stimulated CPB clock has been experimentally implemented and a stability of 7.7 × 10-11at 1 second, 9.6 × 10-13at 1000 second was observed.
We have demonstrated an atomic frequency micrometer based on the coherent population beating phenomenon, which enables us to obtain the beat frequency between the measured signal and the atomic transition frequency. The beat frequency and its fluctuations are detected and accurately measured through digital signal processing, which is capable of up to mHz or higher frequency resolutions (for GHz signal). The frequency discrimination via our method is comparable to that of the Ramsey fringes method, and the working range is no longer limited by the width of line shape. This enables us to achieve an atomic clock by actively compensating the frequency shift, which eliminates the need for a phase locking loop, and broadens the working range with increasing reliability. This novel scheme could be extended to the optical frequency region, implying possible future applications in optical atomic clocks, optical frequency comb, atomic spectroscopy and other related researches.
Coherent population beating (CPB) phenomenon occurs in a typical three-level system. When the frequency difference between two coherent pumping laser fields has a certain detuning from the ground-state hyperfine splitting, the excited state population will experience a transient oscillation before reaching equilibrium, and the oscillation frequency is equal to the detuning. The CPB phenomenon enables us to directly obtain the beat frequency between the measured radio frequency (RF) signal and the atomic transition frequency. Then we can get the standard frequency by compensating the beat frequency to the RF. We propose a scheme to implement atomic clock based on the CPB phenomenon in 2009, and the scheme has been implemented. When this effect is used to achieve an atomic clock, the frequency stability is directly related to the amplitude and SNR (signal to noise ratio) of the CPB signal. Influence of the ground-state hyperfine sublevels' coherence on CPB signal is theoretically simulated and experimentally investigated in this paper. A formula of the CPB signal is derived by using the semi-classical model of the interaction of atoms with light, and the theoretical simulation is done using the formula obtained. In the experiment two coherent pumping laser fields are used to interact with 87Rb atoms. A CPB process includes the coherence build-up and the CPB stimulation. The coherence of the ground-state hyperfine sublevels is achieved by controlling the pumping time of the coherent laser fields that are resonant to the ground-state hyperfine sublevels. With this method, the relationship between CPB signal and coherence of the ground-state hyperfine sublevels can be observed. Result shows that the amplitude of CPB signal is proportional to the ground-state hyperfine sublevels' coherence. The hign quality CPB signal can be achieved when the CPB stimulation is started with a pure coherent population trapping (CPT) state. In the CPB process, the coherence build-up rate is approximately equal to the coherence decay rate. So a 50% duty cycle square wave can be used to modulate the RF, and the period of the square wave had better be twice of the decay time of the ground-state hyperfine sublevels' coherence. To improve the SNR of CPB signal and the stability of atomic frequency standard, the ground-state hyperfine sublevels' coherence must be built up, improved, and maintained before the CPB stimulation. The feasibility of applying CPB phenomenon to the weak magnetic field measurement and other applications is also discussed in this paper.
We proposed a scheme to implement coherent population trapping (CPT) atomic clock based on the transient CPT phenomenon. We proved that the transient transmitted laser power in a typical Λ system near CPT resonance features as a damping oscillation. Also, the oscillating frequency is exactly equal to the frequency detuning from the atomic hyperfine splitting. Therefore, we can directly measure the frequency detuning and then compensated to the output frequency of microwave oscillator to get the standard frequency. By this method, we can further simplify the structure of CPT atomic clock, and make it easier to be digitized and miniaturized.
We demonstrated a digitized atomic clock which is based on the transient oscillation of detuned coherent population trapping (DCPT). In the Λ structure atomic states system, the DCPT oscillation frequency exactly equals the absolute value of the frequency difference between the two pump laser fields minus the two ground states hyperfine splitting frequency. This DCPT atomic clock obtains the standard frequency by adding/subtracting the DCPT frequency from the laser modulation RF frequency. And it does not require a phase locking loop circuit to lock the standard frequency to the atomic transition. In addition, its data processing section can be easily digitized with high accuracy. The frequency instability of 1×10-11/τ1/2(τ=1000s) has been achieved.