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Journal of the Optical Society of America B

Light-shift comparison of electromagnetically induced transparency and coherent population trapping in continuous-wave and Ramsey spectroscopies

Xiaoyan Liu, Xu Zhao, Zhen Xu, Zhengfeng Hu

Published Mar 2, 2021• 2 citations
Publisher

Abstract

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.

DOI
10.1364/josab.411313

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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.
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.
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.
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.
This paper presents a theoretical and experimental investigation on the light shift (AC Stark shift) of the 62S1/2(F = 3 ↔ 4) transition in133Cs, as observed through coherent population trapping (CPT) under a pulsed excitation. The calculated results are good agreement in the experimental results on various parameters and show that the light shift under pulsed excitation is 20∼30 times less than that under continuous excitation. In addition, this paper also presents a two-step pulse method for suppressing the light shift.
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 investigate the application of Ramsey spectroscopy for the development of a microcell atomic clock based on coherent population trapping (CPT). The dependence of the central Ramsey-CPT fringe properties on key experimental parameters is first studied for optimization of the clock’s short-term frequency stability. The sensitivity of the clock frequency to light-shift effects is then studied. In comparison with the continuous-wave (CW) regime case, the sensitivity of the clock frequency to laser power variations is reduced by a factor up to 14 and 40.3 for dark times of 150 and450 μs450~\mu \text{s}450 μs, respectively, at the expense of intensity 3.75 times higher for short-term stability optimization. The dependence of the clock frequency on the microwave power is also reduced in the Ramsey case. We demonstrate that the Ramsey-CPT interrogation improves the clock Allan deviation for averaging times higher than 100 s. With a dark time of450 μs450~\mu \text{s}450 μs, a clock fractional frequency stability of3.8×10−123.8 \times 10^{-12}3.8×10−12at 104s is obtained, in comparison with the level of8×10−118\times 10^{-11}8×10−11obtained in the standard CW case, in similar environmental conditions. These results demonstrate that Ramsey-based interrogation protocols might be an attractive approach for the development of chip-scale atomic clocks (CSACs) with enhanced mid- and long-term stability.