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Acta Physica Sinica

Relationship between coherent population trapping oscillation and Raman detuning

Yan-Chen Han, Yu-Dong Li, Wei Li

Published Oct 12, 2023• 0 citations
Publisher

Abstract

Coherent population trapping (CPT) oscillation is a transient oscillation phenomenon based on the CPT effect, which is related to the Raman detuning of the coherent bichromatic laser fields from the hyperfine ground-states of three-level Λ system. In this work, sawtooth wave is adopted to modulate the frequency of microwave signal to make Raman detuning change uniformly and stepping. Meanwhile, by building the relationship between the microwave frequency modulation rate and the change rate of Raman detuning, the effects of the change rate and mode of Raman detuning on CPT oscillation are analyzed respectively. The results reveal that when the Raman detuning changes uniformly, the CPT oscillation will occur on condition that the change rate is high enough, and the excited oscillations show non-harmonic oscillation behavior. When the Raman detuning is triggered off by step change, the excited CPT oscillation is a damping oscillation, and the oscillation frequency is equal to the frequency of Raman detuning. The modulation of Raman detuning is realized by using sawtooth wave to modulate the microwave frequency, and then the complete establishment of CPT state and the complete attenuation of CPT oscillation process are achieved. This work presents a new modulation method to realize the CPT oscillation, which shows great application potential in the field of weak magnetic measurements and atomic clocks.

DOI
10.7498/aps.73.20231408

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Coherent population trapping (CPT) oscillation is a transient oscillation phenomenon based on the CPT effect, which is related to the Raman detuning of the coherent bichromatic laser fields from the hyperfine ground-states of three-level Λ system. In this work, sawtooth wave is adopted to modulate the frequency of microwave signal to make Raman detuning change uniformly and stepping. Meanwhile, by building the relationship between the microwave frequency modulation rate and the change rate of Raman detuning, the effects of the change rate and mode of Raman detuning on CPT oscillation are analyzed respectively. The results reveal that when the Raman detuning changes uniformly, the CPT oscillation will occur on condition that the change rate is high enough, and the excited oscillations show non-harmonic oscillation behavior. When the Raman detuning is triggered off by step change, the excited CPT oscillation is a damping oscillation, and the oscillation frequency is equal to the frequency of Raman detuning. The modulation of Raman detuning is realized by using sawtooth wave to modulate the microwave frequency, and then the complete establishment of CPT state and the complete attenuation of CPT oscillation process are achieved. This work presents a new modulation method to realize the CPT oscillation, which shows great application potential in the field of weak magnetic measurements and atomic clocks.
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.
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.
The temporal evolution of coherent population trapping (CPT) was observed in rubidium atomic vapor when sudden changes were made to the detuning of a weak Raman field. The subsequent creation and destruction of CPT are caused by the temporal oscillations of optically induced Raman coherence, with their period depending on the Raman detuning. The oscillating signal was observed over a time of order of tens of milliseconds, and the dependence of the relaxation time on the cell temperature and laser power were investigated. The main features of the experimental observations were well explained by the time-dependent density-matrix equations.
Coherent population trapping (CPT) resonance signals have promise in a wide range of applications involving precision sensing. Generally, the CPT phenomenon occurs in a three-level Λ system with a bichromatic phase-coherent light fields. We theoretically and experimentally studied an Rb vapor-cell-based atomic system involving bichromatic CPT optical fields and an external microwave (MW) field simultaneously. In such a mixing scheme, the coherence of the ground states could be controlled either by the Rabi frequency of the microwave field or by the relative phase between the optical fields and the MW field. Moreover, we investigated the Rabi resonance in this mixing scheme. The Rabi frequency of the MW field can be measured SI (International System of Units)-traceably based on the Rabi resonance lineshape, and thus holds the potential to realize intensity stabilization of the optical field in this system. Simple theoretical models and numerical calculations are also presented to explain the experimental results. There is scope to use the proposed technique in future development of SI-traceable optical field strength standards.
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 have theoretically and experimentally proven that the transient transmitted laser power through a typical Λ system atomic cell near Coherent Population Trapping resonance presents as a damping oscillation. The oscillating frequency is identical to the frequency detuning from the atomic hyperfine splitting. Based on the transient coherent population trapping (TCPT) phenomenon, we have proposed an atomic clock in which the standard frequency is obtained by compensated the TCPT oscillating frequency to the RF modulating frequency. Therefore we do not need to lock the RF frequency. There will be advantages for atomic clock miniaturization and stabilization.