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Physical Review A

Measuring state-multipole moments in coherent-population-trapping experiments

Andrew Householder, Nathaniel Ristoff, James C. Camparo

Published Feb 28, 2025• 1 citation
Publisher

Abstract

The traditional Coherent-Population-Trapping (CPT) approach to atomic signal generation in chip-scale atomic clocks (CSACs) requires circularly polarized light, which creates spin polarization in the vapor and leads to reduced CSAC signal-to-noise ratios. Though various strategies have been developed to mitigate this problem, there is only a superficial and/or empirical understanding of these strategies' efficacies due to the difficulty of measuring ground-state population distributions among hyperfine Zeeman sublevels. Here, we demonstrate an optical technique to measure the first three (density-matrix) state multipole moments of a single ground-state hyperfine manifold. Using this technique, we have discovered that ground-state angular momentum alignment (i.e., the quadrupole moment) can play an important role in CPT signal-to-noise ratios.

DOI
10.1103/physreva.111.023715

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The traditional Coherent-Population-Trapping (CPT) approach to atomic signal generation in chip-scale atomic clocks (CSACs) requires circularly polarized light, which creates spin polarization in the vapor and leads to reduced CSAC signal-to-noise ratios. Though various strategies have been developed to mitigate this problem, there is only a superficial and/or empirical understanding of these strategies' efficacies due to the difficulty of measuring ground-state population distributions among hyperfine Zeeman sublevels. Here, we demonstrate an optical technique to measure the first three (density-matrix) state multipole moments of a single ground-state hyperfine manifold. Using this technique, we have discovered that ground-state angular momentum alignment (i.e., the quadrupole moment) can play an important role in CPT signal-to-noise ratios.
Chip-scale atomic clocks (CSACs) based on Coherent Population Trapping (CPT) are at the forefront of next-generation timekeeping for diverse applications, including global navigation satellite systems (GNSS), satellite communications, cell-phone networks, and hand-held GNSS receivers. Notwithstanding the potential ubiquity of this atomic device, a performance-limiting aspect of CSACs is the vapor-phase signal-to-noise ratio (SNR) of their ground-state (mF = 0 to mF = 0) atomic hyperfine resonance. Specifically, in commercially available devices angular-momentum optical pumping “pushes” atomic population towards high |mF| Zeeman sublevels at the expense of population in the 0-0 clock transition. Though mitigation strategies for this SNR limiting process have been proposed and demonstrated there has, to date, been little direct measurement of the population distribution among Zeeman sub-states for atoms undergoing CPT, and how that population distribution is altered by SNR improving mitigation strategies. Here, we describe our initial studies examining this question.
Chip-scale atomic clocks (CSACs) based on Coherent Population Trapping (CPT) are at the forefront of next-generation timekeeping for diverse applications, including global navigation satellite systems (GNSS), satellite communications, cellphone networks, and hand-held GNSS receivers. Notwithstanding the potential ubiquity of this atomic device, a performancelimiting aspect of CSACs is the vapor-phase signal-to-noise ratio (SNR) of their ground-state (mF = 0 to mF = 0) atomic hyperfine resonance. Specifically, in commercially available devices angular-momentum optical pumping “pushes” atomic population towards high |mF| Zeeman sublevels at the expense of population in the 0-0 clock transition. Though mitigation strategies for this SNR limiting process have been proposed and demonstrated there has, to date, been little direct measurement of the population distribution among Zeeman sub-states for atoms undergoing CPT, and how that population distribution is altered by SNR-improving mitigation strategies. Here, we describe our initial studies examining this question.
SummaryCurrent compact atomic clock technologies rely on coherent population trapping (CPT), which employs a microwave resonance to stabilize a crystal oscillator. Standard CPT, while a simple and easy-to-implement optical preparation scheme in alkali metal atoms, suffers from low signal-to-noise ratios (SNR). The primary contributor to the low signal amplitude is the collection of atoms at the extreme ends of the Zeeman sublevels in the hyperfine levels of the alkali ground state, so-called “trap states.” Solutions to the trap-state problem have been reported previously, though the redistribution of atomic population into the CPT signal states with these methods has not yet been carefully examined. This work aims to provide an experimental basis to evaluate trap-state recovery schemes.
SummaryChip-scale atomic clocks (CSAC) are the products of a burgeoning field of miniature precise timing efforts in support of low-SWaP space-qualified timing sources. Most CSACs are based on the coherent population trapping (CPT) effect, which uses laser light to selectively pump atoms into dark states. Because of the multiple accessible and inaccessible hyperfine Zeeman states, many atoms don’t contribute to the signal leading to a low signal-to-noise ratio of the CPT resonance. In turn, clock stability is limited. While solutions to this problem have been studied previously, the examination of the redistribution of atoms through the novel pumping solutions has not been thoroughly studied. This work provides continued exploration of an experimental effort to evaluate Zeeman end-state recovery schemes.
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 have developed and experimentally studied a coherent population trapping (CPT) state preparation scheme for atomic clock application with co-propagating left and right circularly polarized lasers. With realization of constructive interference and spin-polarized dark state free in CPT state preparation, we have obtained CPT resonance signal 3 times larger than that of the conventional scheme used in atomic clock. Polarization fluctuations and CPT signal sensitivity to laser power behaviors are both improved with the scheme. Our study reveals that it is a promising candidate for both normal-size and chip-scale CPT atomic clocks.