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Europhysics Letters (EPL)

Noise cancellation in transient coherent population trapping by differential detection

Lin Dan, Yaoyuan Fan, Yuxin Zhuang, Zhong Wang, Jianye Zhao

Published Jul 21, 2020• 3 citations
Publisher

Abstract

We report a damped coherent population trapping (CPT) process, which has the very same mechanism as the coherent population beating (CPB). A differential CPB scheme is proposed based on the optical path delay, through which the left- and right-hand circularly polarized lights are modulated with a phase difference of π/2. The CPB signals oscillate with the frequency in a radio frequency (RF) range, which makes the detuning frequency equal to the splitting frequency between the hyperfine energy level of the ground state of cesium. The differential CPB signal with non-zero amplitude is obtained after the two signals being subtracted from each other, thereby improving the signal-to-noise ratio of the CPB. The measurements are explained well with a simple, four-level model and are interpreted as a simple harmonic oscillator interaction with four light fields. The Allan variance of the CPB atomic clock is measured in the conventional and the differential detection configurations. The 1- s stability of the differential CPB scheme is , which is better than that of under the conventional configuration. The results confirm that the differential CPB scheme can improve the signal-to-noise ratio and hence the short-term stability.

DOI
10.1209/0295-5075/130/60004

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Europhysics Letters (EPL)•Jul 1, 2017•11 citations
We report a damped coherent population trapping (CPT) process, which has the very same mechanism as the coherent population beating (CPB). A differential CPB scheme is proposed based on the optical path delay, through which the left- and right-hand circularly polarized lights are modulated with a phase difference of π/2. The CPB signals oscillate with the frequency in a radio frequency (RF) range, which makes the detuning frequency equal to the splitting frequency between the hyperfine energy level of the ground state of cesium. The differential CPB signal with non-zero amplitude is obtained after the two signals being subtracted from each other, thereby improving the signal-to-noise ratio of the CPB. The measurements are explained well with a simple, four-level model and are interpreted as a simple harmonic oscillator interaction with four light fields. The Allan variance of the CPB atomic clock is measured in the conventional and the differential detection configurations. The 1- s stability of the differential CPB scheme is , which is better than that of under the conventional configuration. The results confirm that the differential CPB scheme can improve the signal-to-noise ratio and hence the short-term stability.
We present a digital differential detection scheme using a single photodiode to suppress the diode laser frequency noise and improve the short-term stability in atomic clocks based on coherent population trapping (CPT) resonance. One laser light is divided into two beams via modulation of an acousto-optic modulator. One beam induces CPT resonance with circularly polarized light, and the other beam induces only absorption with linearly polarized light. A differential algorithm counteracts common-mode noise from the two beams. A stability of 6.86×10−12 at 100 s and 2.26×10−12 at 1000 s has been demonstrated. The short-term stability is improved by a factor of 2.4 at 100 s. The scheme promises to eliminate laser-related noise and explore potential applications in chip-scale atomic clocks.
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.
Traditional coherent population trapping (CPT) atomic clocks use single circularly polarized coherent multichromatic light to interact with atoms for preparing CPT dark states. While this configuration is simple, it suffers from the trap states and involves only the ±1st-order sidebands in the CPT resonance, excluding the carrier and other sidebands. This results in a lower CPT signal amplitude and higher laser noise, limiting the frequency stability of CPT atomic clocks. To address this issue, we developed and experimentally validated a scheme utilizing left- and right-circularly polarized light based on multiple coherent superpositions. This scheme significantly enhances the amplitude of the CPT resonance. Furthermore, by incorporating a Michelson interferometer, the polarization direction of the ±1st-order sidebands in the coherent multichromatic light is adjusted from parallel to perpendicular, enabling the filtering of one sideband to be detected while eliminating other unwanted sidebands and effectively suppressing laser noise. The results show that, under identical conditions, the short-term frequency stability of this method is theoretically improved by a factor of seven compared to the traditional circularly polarized light scheme, providing an effective pathway for the development of high-performance CPT atomic clocks.
We present preliminary results showing that some noise sources in vapor cell atomic clocks based on coherent population trapping (CPT) can be suppressed with differential detection. The scheme we propose differs from more conventional differential detection in that both optical fields pass through the alkali vapor cell but have different polarizations, one circular and one linear. Because CPT resonances are only excited by the circularly polarized beam, the linearly polarized beam can be used to reduce several important sources of noise. With this technique, we demonstrate reduction of the short-term frequency instability of a CPT atomic frequency reference by a factor of about 1.5.
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.
A scheme is investigated for a coherent population trapping (CPT) atomic clock, wherein the polarization of a beam produced by a vertical-cavity surface-emitting laser is converted to an elliptically polarized beam that interacts with alkali atoms, where the CPT signal is extracted by differentially detecting the magneto-optically rotated light within the transmitted beam. The scheme eliminates the spin-polarized trap state of the atoms and the unwanted background signal, and suppresses in the CPT signal the noise converted from the laser noise. This result reveals the promise of this scheme for realizing a compact CPT atomic clock possessing a significantly improved frequency stability compared to current compact CPT atomic clock devices, coupled with similar power consumption, volume, and cost therewith.