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Applied Physics Letters

Inhomogeneous light shifts of coherent population trapping resonances

J. W. Pollock, Valeriy I. Yudin, А. В. Тайченачев, M. Yu. Basalaev, Д. В. Коваленко, Azure Hansen, John E. Kitching, William McGehee

Published Apr 11, 2022• 11 citations
Publisher

Abstract

Coherent population trapping (CPT) in atomic vapors using all-optical interrogation has enabled the miniaturization of microwave atomic clocks. Light shifts induced by the CPT driving fields can impact the spectral profile of CPT resonances and are a common limit to the long-term stability of CPT clocks. Nonlinear light shifts have been observed in several CPT systems and have not been explored in detail. In this Letter, we demonstrate that nonlinear light shifts in CPT clocks can arise from spatially inhomogeneous CPT driving fields. We measure this effect using Gaussian laser beams in a buffer gas cell and show strong agreement with a four-level model describing the CPT Λ-system with a noninteracting “trap” state. We estimate the effect of this nonlinearity on recently developed light shift mitigation techniques and suggest improvements to existing techniques.

DOI
10.1063/5.0087391

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Coherent population trapping (CPT) in atomic vapors using all-optical interrogation has enabled the miniaturization of microwave atomic clocks. Light shifts induced by the CPT driving fields can impact the spectral profile of CPT resonances and are a common limit to the long-term stability of CPT clocks. Nonlinear light shifts have been observed in several CPT systems and have not been explored in detail. In this Letter, we demonstrate that nonlinear light shifts in CPT clocks can arise from spatially inhomogeneous CPT driving fields. We measure this effect using Gaussian laser beams in a buffer gas cell and show strong agreement with a four-level model describing the CPT Λ-system with a noninteracting “trap” state. We estimate the effect of this nonlinearity on recently developed light shift mitigation techniques and suggest improvements to existing techniques.
We study the field shift of coherent population trapping (CPT) resonance excited by a bichromatic field in an open Λ system with account for the Gaussian profile of the laser radiation intensity. Two methods for error signal formation are considered: the harmonic frequency modulation and the step phase modulation (phase jumps). It is shown that the spatial inhomogeneity of the light beam leads to an essentially nonlinear dependence of the error signal shift on the laser radiation intensity. We propose an approach for the linearization of this dependence, which is important for the development of methods for suppressing the field shift in atomic clocks based on CPT resonances.
Abstract We study the field shift of coherent population trapping (CPT) resonance excited by a bichromatic field in an open Λ system with account for the Gaussian profile of the laser radiation intensity. Two methods for error signal formation are considered: the harmonic frequency modulation and the step phase modulation (phase jumps). It is shown that the spatial inhomogeneity of the light beam leads to an essentially nonlinear dependence of the error signal shift on the laser radiation intensity. We propose an approach for the linearization of this dependence, which is important for the development of methods for suppressing the field shift in atomic clocks based on CPT resonances.
State-of-the-art miniature atomic clocks (MACs) are based on the phenomenon of coherent population trapping (CPT) in alkali-metal atomic vapors (Rb\mathrm{Rb}Rb or Cs\mathrm{Cs}Cs). Improving the stability of the clock frequency is a crucial issue; resolving it would result in significant progress in numerous applications. Here, we examine the configuration of the light field, which is composed of two bichromatic beams with opposing handedness of circular polarization. The beams are in resonance with optical transitions in the Cs\mathrm{Cs}Cs D1{D}_{1}D1​ line ($\ensuremath{\lambda}\ensuremath{\approx}895$ nm). This configuration has previously been shown to produce observed CPT resonances with higher contrast than a standard single-beam scheme; however, our scheme implements pump and probe beams that operate independently, with the transmission of the probe beam being monitored separately. This approach differs from previous studies. The experiments are carried out using a cubic $5\ifmmode\times\else\texttimes\fi{}5\ifmmode\times\else\texttimes\fi{}5\phantom{\rule{0.2em}{0ex}}{\mathrm{mm}}^{3}$ vapor cell filled with buffer gas. It is shown that the line shape of the resonance acquires an asymmetry that can be efficiently controlled by a microwave (Raman) phase between the beams. As a proof of concept, we study the way in which this asymmetry can help to mitigate the influence of the ac Stark (light) shift on the long-term frequency stability of CPT clocks based on vapor microcells ($V\ensuremath{\ll}1\phantom{\rule{0.2em}{0ex}}{\mathrm{cm}}^{3}$). Experimental verification is performed with both a distributed-Bragg-reflector laser and a vertical-cavity surface-emitting laser. The latter is of particular importance for the development of MACs. The experimental results are in qualitative agreement with the analytical theory based on a double-$\mathrm{\ensuremath{\Lambda}}$ scheme of atomic energy levels.
Vapor cell atomic clocks exhibit reduced frequency stability for averaging time between about one hundred and a few thousand seconds. Here we report a study on the impact of the main parameters on the mid-to-long term instability of a buffer-gas vapor cell Cs clock, based on coherent population trapping (CPT). The CPT signal is observed on the Cs D1 line transmission, using a double Λ scheme and a Ramsey interrogation technique. The effects on the clock frequency of the magnetic field, the cell temperature, and the laser intensities are reported. We show in particular that the laser intensity shift is temperature dependent. Along with the laser intensity ratio and laser polarization properties, this is one of the most important parameters.
The authors demonstrate a simple technique to significantly improve the long-term frequency stability of atomic clocks based on coherent population trapping (CPT). In this technique, the CPT fields are created by a modulated diode laser and a slow servo is used to actively tune the laser modulation index to a value where the light shift vanishes. The observed clock frequency at this modulation index is given by the rubidium hyperfine frequency when no light fields are present, and this makes the clock frequency largely insensitive to variations in laser properties. In addition to reducing stringent requirements on the long-term stabilities of laser temperature, laser frequency, and rf modulation power, this technique may also significantly reduce frequency drifts related to laser aging. In the experiment, they demonstrate improvement by over one order of magnitude in the stability of a clock that is limited by light-shift-induced frequency drifts.