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Optical and Quantum Sensing and Precision Metrology II

Measuring multipole moments of the CPT density matrix during optical polarization modulation

Zachary Warren, James C. Camparo

Published Mar 3, 2022• 2 citations
Publisher

Abstract

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.

DOI
10.1117/12.2616925

Related papers

Measuring Multipole Moments of the CPT Density Matrix Under Optical Field Polarization-Modulation Conditions

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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.

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

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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.

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Multipole Moments of the CPT Density Matrix in Polarization Modulation Conditions

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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.

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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.

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Moustafa Abdel Hafiz, Rodolphe Boudot

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Journal of Applied Physics•Sep 28, 2015•49 citations

Feasibility toward a compact high performance coherent population trapping clock

Peter Yun, François Tricot, Emeric de Clercq +4 more

We demonstrate a vapor-cell atomic-clock prototype based on a continuous-wave interrogation and double-modulation coherent population trapping (DM-CPT) technique. The DM-CPT technique uses a synchronous modulation of polarization and the relative phase of a bichromatic laser beam in order to increase the number of atoms trapped in a dark state, i.e., a nonabsorbing state. The narrow resonance, observed in the transmission of a Cs vapor cell, is used as a narrow frequency discriminator in an atomic clock. A detailed characterization of the CPT resonance versus numerous parameters is reported. A short-term fractional-frequency stability of 3.2×10−13τ−1/2 up to a 100-s averaging time is measured. These performances are more than one order of magnitude better than industrial Rb clocks and are comparable to those of the best laboratory-prototype vapor-cell clocks. The noise-budget analysis shows that the short- and midterm frequency stability is mainly limited by the power fluctuations of the microwave used to generate the bichromatic laser. These preliminary results demonstrate that the DM-CPT technique is well suited for the development of a high-performance atomic clock, with the potential compact and robust setup due to its linear architecture. This clock could find future applications in industry, telecommunications, instrumentation, or global navigation satellite systems.

•Apr 14, 2019•0 citations
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.
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.
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.
This article reports on the characterization of a compact coherent-population-trapping (CPT) Cs vapor cell atomic clock using the push-pull optical pumping technique. This method allows to detect high-contrast CPT resonances on the 0-0 magnetic-field insensitive clock transition. The clock short-term fractional frequency stability is measured to be 3×10−13 τ−1/2 up to 100 s averaging time, in correct agreement with the signal-to-noise ratio limit. These results are among the best performances ever reported for a CPT-based clock. The noise budget is detailed. A preliminary study is reported to evaluate limitations to the clock mid-term frequency stability. The clock performances are found to be presently mainly limited in the mid-term by laser power effects.
We demonstrate a vapor-cell atomic-clock prototype based on a continuous-wave interrogation and double-modulation coherent population trapping (DM-CPT) technique. The DM-CPT technique uses a synchronous modulation of polarization and the relative phase of a bichromatic laser beam in order to increase the number of atoms trapped in a dark state, i.e., a nonabsorbing state. The narrow resonance, observed in the transmission of a Cs vapor cell, is used as a narrow frequency discriminator in an atomic clock. A detailed characterization of the CPT resonance versus numerous parameters is reported. A short-term fractional-frequency stability of 3.2×10−13τ−1/2 up to a 100-s averaging time is measured. These performances are more than one order of magnitude better than industrial Rb clocks and are comparable to those of the best laboratory-prototype vapor-cell clocks. The noise-budget analysis shows that the short- and midterm frequency stability is mainly limited by the power fluctuations of the microwave used to generate the bichromatic laser. These preliminary results demonstrate that the DM-CPT technique is well suited for the development of a high-performance atomic clock, with the potential compact and robust setup due to its linear architecture. This clock could find future applications in industry, telecommunications, instrumentation, or global navigation satellite systems.