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Chinese Physics B

Light-shift induced by two unbalanced spontaneous decay rates in EIT (CPT) spectroscopies under Ramsey pulse excitation*

Xiaoyan Liu, Xu Zhao, J. Sun, Zhen Xu, Zhengfeng Hu

Published May 26, 2021• 4 citations
Publisher

Abstract

Light shift is important and inevitably affects the long-term stability of an atomic clock. In this work, considering two unbalanced branches of the spontaneous decay rate in a three-level system, we studied the frequency shifts of electromagnetically induced transparency (EIT) and coherent population trapping (CPT) clocks operating under the pulse sequence regime by numerically solving the Liouville density matrix equations. The results show that the frequency shifts are larger when the two branches of spontaneous emission rate are not equal compared to the equal case. In addition, in EIT-Ramsey, the effect of the unbalanced branches of the spontaneous decay rate and relaxations of low-energy states on the frequency shift is greater than that of Rabi frequency. In CPT-Ramsey, the relaxations of low-energy states play a dominant role in frequency shift.

DOI
10.1088/1674-1056/ac0528

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Light shift is important and inevitably affects the long-term stability of an atomic clock. In this work, considering two unbalanced branches of the spontaneous decay rate in a three-level system, we studied the frequency shifts of electromagnetically induced transparency (EIT) and coherent population trapping (CPT) clocks operating under the pulse sequence regime by numerically solving the Liouville density matrix equations. The results show that the frequency shifts are larger when the two branches of spontaneous emission rate are not equal compared to the equal case. In addition, in EIT-Ramsey, the effect of the unbalanced branches of the spontaneous decay rate and relaxations of low-energy states on the frequency shift is greater than that of Rabi frequency. In CPT-Ramsey, the relaxations of low-energy states play a dominant role in frequency shift.
In the atomic frequency standard, the light shift inevitably affects the long-term stability of the atomic clock. In this work, we accurately calculated the light shifts of electromagnetically induced transparency (EIT) and coherent population trapping (CPT) clocks operating under continuum and pulse sequence regimes by numerically solving the Liouville density matrix equation, including all the relaxation terms of a three-level system. The results show that the light shifts under pulse excitation are smaller than those under continuous excitation and the light shifts of the CPT process are much smaller than those of the EIT process under both excitations. It is also found that the light shifts in the continuous excitation increase and those in the pulse excitation decrease with an increase in the Rabi frequency. The light shifts will increase with an increase of the relaxations of the ground states for both the processes under both regimes. Compared to all process atomic clocks, the light shift of pulse-excited atomic clocks is the smallest, which will be suitable for many applications.
This study aimed to detect the light shift by utilizing various atomic resonances observed under pulsed excitation with drive current modulation (DCM). Light shift degrades the performance of atomic clocks, and several studies have attempted to mitigate or correct it. Pulsed excitation with DCM facilitates the observation of various Ramsey-coherent population trapping (CPT) resonances owing to wavelength variation. Further, in the Ramsey-CPT sequence, a semi-continuous wave CPT resonance (SCW-CPT resonance), which is a continuous wave CPT resonance from pulsed lasers, is also observed. As these atomic resonances exhibit different frequency sensitivities to laser intensity, the frequency shifts differ based on the changes in laser intensity. This facilitates the detection of the light shift. By simultaneously measuring the resonance frequencies of two Ramsey-CPT resonances and the SCW-CPT resonance while varying the laser intensity to induce light shifts, we measured the resulting frequency changes. Each resonance exhibited a different frequency shift in response to the light shift. Therefore, this study conformed the feasibility of detecting and estimating the light shift in an operational atomic clock.
Abstract Light shifts induced during atom–light interactions significantly affect the medium- and long-term frequency stability of atomic clocks. Here, we employ composite laser pulse sequences to mitigate interrogation-induced light shifts in a cold-atom coherent-population-trapping clock. We obtain the anti-symmetry error signal via modulating the local oscillator phase in the free-evolution time of Ramsey interferometry. Utilizing this signal, we employ two feedback loops to simultaneously eliminate light shifts and stabilize the clock frequency using the auto-balanced Ramsey (ABR) spectroscopy scheme. Our experimental results demonstrate that this approach can reduce the clock frequency’s sensitivity to variations in light shifts by implementing four Ramsey sub-sequences. Furthermore, we show that the ABR spectroscopy scheme enhances the long-term frequency stability of the atomic clock when the averaging time τ > 5000 s.
We both numerically and analytically investigate on the light shift in Ramsey-CPT resonance for compact atomic clocks. The numerical calculation of the light shift is based on a density matrix analysis in Λ-type three state model. And the analytical method leads to an estimation equation of light shift in the Raman-Ramsey scheme. The estimation equation expresses the relationship between light shift and all pulse parameters. The results show that the estimation equation was reproduced well as the numerical results.
Coherent-population trapping (CPT) is a multilevel quantum coherence phenomenon of promising applications in atomic clocks and magnetometers. In particular, multipulse CPT Ramsey interferometry is a powerful tool for improving the performance of CPT atomic clocks. Most studies on multipulse CPT Ramsey interferometry consider periodic pulse sequence and time-independent detuning. However, to further improve the accuracy and precision, one may modify the spectrum symmetry which involves a pulse sequence with time-dependent detuning or phase shift. Here we theoretically analyze the multipulse CPT Ramsey interferometry under arbitrary pulse sequences of time-dependent detuning and obtain a general analytical formula. Using our formula, we analyze the popular CPT Ramsey interferometry schemes such as two-pulse symmetric and antisymmetric spectroscopy and multipulse symmetric and antisymmetric spectroscopy. Under periodic pulses, we quantitatively obtain the influences of pulse width, pulse period, pulse number, and Rabi frequency. Furthermore, we examine the impact of CPT pulses and Rabi frequency on the light shift in both two-pulse and multipulse CPT Ramsey interference. Our theoretical results can guide the experimental design to improve the performance of atomic clocks via multipulse CPT Ramsey interferometry.
We investigate theoretically the time dependent fluorescence spectra (TDFS) of a three-level system in electromagnetically induced transparency (EIT) and coherent population trapping (CPT) configurations. Time dependent fluorescence intensities of Rayleigh and Stokes transitions are studied as a function of the ground state coherence relaxation rate and initial state preparation, and their correlation with the temporal evolution of dark and bright states is established. Linewidths of fluorescence and absorption are compared in different regimes of relaxation rates. The results are used to discuss the characteristic features of EIT and CPT in the domain of fluorescence spectroscopy.