© 2026 Aqora Quantum S.A.S.

Terms Privacy Legal Notice

Physical Review Applied

Quantum sensitivity limits and dynamical correlations in alkali-vapor sensors

K. Mouloudakis, V. Koutrouli, I.K. Kominis, M.W. Mitchell, G. Vasilakis

Published Dec 11, 2025• 3 citations

Abstract

For spin-polarized ensembles of alkali-metal atoms with hyperfine structure and spin greater than 1/2, the interplay between spin dynamics and quantum noise mechanisms remains largely unexplored, especially in the spin-exchange-relaxation-free (SERF) regime. In particular, the theoretical understanding of the dynamics for the mean values of the spin operators was established shortly after the advent of optical pumping. In contrast, a corresponding theory for spin fluctuations has not yet been developed, and is addressed in this work. Here, we develop such a first-principles theory of spin fluctuations in alkalimetal vapors. The nonlinearity bottleneck of spin-exchange collisions, which dominate the physics of such vapors, is overcome by linearizing the dynamics around the equilibrium density matrix. The result is a precise calculation of the absolute magnetic sensing limit of optically pumped atomic magnetometers, which can precisely benchmark quantum limited and quantum enhanced protocols, in contrast to the traditional approach shown to be adequate only within a factor of 2. Further, we elucidate how signal and noise in atomic magnetometers are distributed among the spin eigenmodes defined under continuous optical pumping and probing via the paramagnetic Faraday rotation. Notably, in the SERF regime, alongside the magnetic resonance narrowing, we find a reduction of spin noise at the spin-precession frequency as a consequence of strong hyperfine correlations redistributing spin noise, when both hyperfine manifolds are simultaneously probed. These insights can lead to improved quantum devices utilizing alkali-metal atoms or similar spin-based sensing platforms.

DOI: 10.1103/mbdq-md8f

Related papers

Spin projection noise and the magnetic sensitivity of optically pumped magnetometers

K. Mouloudakis, V. Koutrouli, Iannis K. Kominis +2 more

Present protocols for obtaining the ultimate magnetic sensitivity of optically pumped magnetometers (OPMs) utilizing alkali-metal ensembles rely on uncorrelated atoms in stretched states. A new approach for calculating the spin projection noise (SPN)-limited signal to noise ratio (SNR) and the magnetic sensitivity of OPMs is proposed. Our model is based solely on the mean-field density matrix dynamics and in contrast to previous models, it applies to both low and high field regimes, it takes into account the degree of spin polarization, the intra- and interhyperfine correlations, the decoherence processes, the atom-light coupling and the effects of the spin dynamics on the spin-noise spectra. Fine tuning of the probe frequency allow us to explore different hyperfine states and ground-state correlations. Especially in the spin-exchange-relaxation-free (SERF) regime, alongside the magnetic resonance narrowing and the increased number density, hallmarks of SERF magnetometers, we report on a new SERF feature; the reduction of spin-projection noise at the spin precession frequency as a consequence of strongly-correlated hyperfine spins that attenuate and redistribute SPN when properly probed.

arXiv:2402.10746•Feb 16, 2024•0 citations

Spin dynamics and noise spectrum for alkali-metal atoms of arbitrary polarization in the spin-exchange-relaxation-free regime

Yang Li, Xiangyu Li, Tingxuan Guo +1 more

Theoretical studies on the spin dynamics of hot alkali-metal vapors typically require numerical simulations of the density-matrix equation, which is nonlinear because of spin-exchange collisions. In this study we derive a set of effective hyperfine Bloch equations (EHBEs) for systems with arbitrary polarization in the spin-exchange-relaxation-free (SERF) regime. These EHBEs provide an intuitive framework for understanding the spin dynamics in the SERF regime and yield simple solutions that are in excellent agreement with the results of density-matrix simulations. A stochastic EHBE model is created by adding spin noise caused by fundamental quantum fluctuations. This yields an optical-spin-noise spectrum that includes the intrinsic spin-projection noise and the backaction light-shift noise from Faraday rotation measurements. The spectrum is a summation of several absorptive and dispersive components, each of which has a clear physical origin and a simple algebraic expression. This provides a benchmark for calibrating future spin-squeezing experiments in the SERF regime.

Physical Review A•Mar 7, 2025•5 citations

Effects of spin-exchange collisions on the fluctuation spectra of hot alkali-metal vapors

K. Mouloudakis, Georgios Vasilakis, Vito Giovanni Lucivero +3 more

We present a first-principles analysis of the noise spectra of alkali-metal vapors in and out of the spin-exchange-relaxation-free (SERF) regime, and we predict nonintuitive features with a potential to further improve the sensitivity of SERF media, and which must be taken into account in their use in quantum optical applications. Studying the process of spin-noise spectroscopy (SNS), we derive analytic formulas for the observable noise spectra, and for the correlation functions among different hyperfine components, which give additional insight into the spin dynamics. The analytic results indicate a variety of distortions of the spin-noise spectrum relative to simpler models, including a broad spectral background that mimics optical shot noise, interference of noise contributions from the two ground-state hyperfine levels, noise reduction at the spin-precession frequency, and ``hiding'' of spin-noise power that can introduce a systematic error in noise-based calibrations, e.g., for spin-squeezing experiments.

arXiv:2204.08748•Physical Review A•Aug 15, 2022•25 citations

Spin-exchange-relaxation-free magnetometry with Cs vapor

M. P. Ledbetter, Igor Savukov, Víctor M. Acosta +2 more

We describe a Cs atomic magnetometer operating in the spin-exchange-relaxation-free (SERF) regime. With a vapor cell temperature of $103\text{ }\ifmmode^\circ\else\textdegree\fi{}\text{C}$ we achieve intrinsic magnetic resonance widths $\ensuremath{\Delta}B=17\text{ }\ensuremath{\mu}\text{G}$ corresponding to an electron spin-relaxation rate of $300\text{ }{\text{s}}^{\ensuremath{-}1}$ when the spin-exchange rate is ${\ensuremath{\Gamma}}_{\text{SE}}=14\text{ }000\text{ }{\text{s}}^{\ensuremath{-}1}$. We also observe an interesting narrowing effect due to diffusion. Signal-to-noise measurements yield a sensitivity of about $400\text{ }\text{pG}/\sqrt{\text{Hz}}$. Based on photon shot noise, we project a sensitivity of $40\text{ }\text{pG}/\sqrt{\text{Hz}}$. A theoretical optimization of the magnetometer indicates sensitivities on the order of $2\text{ }\text{pG}/\sqrt{\text{Hz}}$ should be achievable in a $1\text{ }{\text{cm}}^{3}$ volume. Because Cs has a higher saturated vapor pressure than other alkali metals, SERF magnetometers using Cs atoms are particularly attractive in applications requiring lower temperatures.

arXiv:0708.1012•Physical Review A•Mar 13, 2008•400 citations

All-Optical Broadband Atomic Magnetometer Utilizing Raman-Driven Spin Noise Spectroscopy

Sayari Majumder, Saptarishi Chaudhuri

We report the development and performance of an atomic magnetometer (AM) utilizing the Raman-driven spin noise spectroscopy (RDSNS) technique, which measures the intrinsic spin fluctuations of an atomic medium subjected to a coherent two-photon optical drive. The RDSNS signal is noninvasively detected using a far-off resonant weak probe light utilizing a polarimetric detection scheme. This overcomes the limitations of the small dynamic range and low bandwidth of traditional optically pumped magnetometers (OPMs) or AMs operating in the spin exchange relaxation-free (SERF) regime. We experimentally demonstrate, using both paraffin-coated and buffer-gas-filled vapor cell containing neutral rubidium atoms, that the dynamic range of such magnetometers can reach beyond 150 G while maintaining a dc magnetometer resolution of around 30 pT and a magnetic noise sensitivity of around$30~\text {pT}/\sqrt {\text {Hz}}$at a bandwidth of 100 Hz and a magnetic field of about 0.6 mT. Being an all-optical setup, this instrument is largely immune to interference with stray radio frequency fields and has the potential to be miniaturized and field deployable. One of the practical applications would be to measure variations in geomagnetic fields precisely without having to shield the magnetometer.

IEEE Transactions on Instrumentation and Measurement•Jan 1, 2025•6 citations

Dynamically Polarized SERF Atomic Comagnetometer

Xiaofei Huang, Wei, Kai, Rui Yang +4 more

Atomic spin sensors are essential for beyond-the-standard-model exploration, biomagnetic measurement, and quantum navigation. While the traditional DC mode spin-exchange relaxation-free (SERF) comagnetometer achieves ultrahigh sensitivity, further improvements require suppressing technical noise and surpassing standard quantum limit. In this work, we develop a K-Rb-$^{21}$Ne SERF atomic comagnetometer that dynamically polarizes the electron and nuclear spins, shielding signals from direct interference by pump light. We establish a three-phase evolutionary model for hybrid spin ensemble dynamics, yielding a complete analytical solution, and analyze the responses to various spin perturbations. Additionally, we achieve an averaged 38.5 $\%$ suppression of the polarization noise and identify the key factors that limit sensitivity improvements. The dynamically polarized comagnetometer exhibits effective suppression of technical noise and holds the potential to overcome quantum noise limit, while offering promising applications in exploring new physics and precise magnetic field measurements.

arXiv:2505.18462•May 24, 2025•0 citations

For spin-polarized ensembles of alkali-metal atoms with hyperfine structure and spin greater than 1/2, the interplay between spin dynamics and quantum noise mechanisms remains largely unexplored, especially in the spin-exchange-relaxation-free (SERF) regime. In particular, the theoretical understanding of the dynamics for the mean values of the spin operators was established shortly after the advent of optical pumping. In contrast, a corresponding theory for spin fluctuations has not yet been developed, and is addressed in this work. Here, we develop such a first-principles theory of spin fluctuations in alkalimetal vapors. The nonlinearity bottleneck of spin-exchange collisions, which dominate the physics of such vapors, is overcome by linearizing the dynamics around the equilibrium density matrix. The result is a precise calculation of the absolute magnetic sensing limit of optically pumped atomic magnetometers, which can precisely benchmark quantum limited and quantum enhanced protocols, in contrast to the traditional approach shown to be adequate only within a factor of 2. Further, we elucidate how signal and noise in atomic magnetometers are distributed among the spin eigenmodes defined under continuous optical pumping and probing via the paramagnetic Faraday rotation. Notably, in the SERF regime, alongside the magnetic resonance narrowing, we find a reduction of spin noise at the spin-precession frequency as a consequence of strong hyperfine correlations redistributing spin noise, when both hyperfine manifolds are simultaneously probed. These insights can lead to improved quantum devices utilizing alkali-metal atoms or similar spin-based sensing platforms.

Present protocols for obtaining the ultimate magnetic sensitivity of optically pumped magnetometers (OPMs) utilizing alkali-metal ensembles rely on uncorrelated atoms in stretched states. A new approach for calculating the spin projection noise (SPN)-limited signal to noise ratio (SNR) and the magnetic sensitivity of OPMs is proposed. Our model is based solely on the mean-field density matrix dynamics and in contrast to previous models, it applies to both low and high field regimes, it takes into account the degree of spin polarization, the intra- and interhyperfine correlations, the decoherence processes, the atom-light coupling and the effects of the spin dynamics on the spin-noise spectra. Fine tuning of the probe frequency allow us to explore different hyperfine states and ground-state correlations. Especially in the spin-exchange-relaxation-free (SERF) regime, alongside the magnetic resonance narrowing and the increased number density, hallmarks of SERF magnetometers, we report on a new SERF feature; the reduction of spin-projection noise at the spin precession frequency as a consequence of strongly-correlated hyperfine spins that attenuate and redistribute SPN when properly probed.

Theoretical studies on the spin dynamics of hot alkali-metal vapors typically require numerical simulations of the density-matrix equation, which is nonlinear because of spin-exchange collisions. In this study we derive a set of effective hyperfine Bloch equations (EHBEs) for systems with arbitrary polarization in the spin-exchange-relaxation-free (SERF) regime. These EHBEs provide an intuitive framework for understanding the spin dynamics in the SERF regime and yield simple solutions that are in excellent agreement with the results of density-matrix simulations. A stochastic EHBE model is created by adding spin noise caused by fundamental quantum fluctuations. This yields an optical-spin-noise spectrum that includes the intrinsic spin-projection noise and the backaction light-shift noise from Faraday rotation measurements. The spectrum is a summation of several absorptive and dispersive components, each of which has a clear physical origin and a simple algebraic expression. This provides a benchmark for calibrating future spin-squeezing experiments in the SERF regime.

We present a first-principles analysis of the noise spectra of alkali-metal vapors in and out of the spin-exchange-relaxation-free (SERF) regime, and we predict nonintuitive features with a potential to further improve the sensitivity of SERF media, and which must be taken into account in their use in quantum optical applications. Studying the process of spin-noise spectroscopy (SNS), we derive analytic formulas for the observable noise spectra, and for the correlation functions among different hyperfine components, which give additional insight into the spin dynamics. The analytic results indicate a variety of distortions of the spin-noise spectrum relative to simpler models, including a broad spectral background that mimics optical shot noise, interference of noise contributions from the two ground-state hyperfine levels, noise reduction at the spin-precession frequency, and ``hiding'' of spin-noise power that can introduce a systematic error in noise-based calibrations, e.g., for spin-squeezing experiments.

We describe a Cs atomic magnetometer operating in the spin-exchange-relaxation-free (SERF) regime. With a vapor cell temperature of $103\text{ }\ifmmode^\circ\else\textdegree\fi{}\text{C}$ we achieve intrinsic magnetic resonance widths $\ensuremath{\Delta}B=17\text{ }\ensuremath{\mu}\text{G}$ corresponding to an electron spin-relaxation rate of $300\text{ }{\text{s}}^{\ensuremath{-}1}$ when the spin-exchange rate is ${\ensuremath{\Gamma}}_{\text{SE}}=14\text{ }000\text{ }{\text{s}}^{\ensuremath{-}1}$. We also observe an interesting narrowing effect due to diffusion. Signal-to-noise measurements yield a sensitivity of about

400\text{ }\text{pG}/\sqrt{\text{Hz}}

. Based on photon shot noise, we project a sensitivity of

40\text{ }\text{pG}/\sqrt{\text{Hz}}

. A theoretical optimization of the magnetometer indicates sensitivities on the order of

2\text{ }\text{pG}/\sqrt{\text{Hz}}

should be achievable in a

1\text{ }{\text{cm}}^{3}

volume. Because Cs has a higher saturated vapor pressure than other alkali metals, SERF magnetometers using Cs atoms are particularly attractive in applications requiring lower temperatures.

We report the development and performance of an atomic magnetometer (AM) utilizing the Raman-driven spin noise spectroscopy (RDSNS) technique, which measures the intrinsic spin fluctuations of an atomic medium subjected to a coherent two-photon optical drive. The RDSNS signal is noninvasively detected using a far-off resonant weak probe light utilizing a polarimetric detection scheme. This overcomes the limitations of the small dynamic range and low bandwidth of traditional optically pumped magnetometers (OPMs) or AMs operating in the spin exchange relaxation-free (SERF) regime. We experimentally demonstrate, using both paraffin-coated and buffer-gas-filled vapor cell containing neutral rubidium atoms, that the dynamic range of such magnetometers can reach beyond 150 G while maintaining a dc magnetometer resolution of around 30 pT and a magnetic noise sensitivity of around

30~\text {pT}/\sqrt {\text {Hz}}

at a bandwidth of 100 Hz and a magnetic field of about 0.6 mT. Being an all-optical setup, this instrument is largely immune to interference with stray radio frequency fields and has the potential to be miniaturized and field deployable. One of the practical applications would be to measure variations in geomagnetic fields precisely without having to shield the magnetometer.

Atomic spin sensors are essential for beyond-the-standard-model exploration, biomagnetic measurement, and quantum navigation. While the traditional DC mode spin-exchange relaxation-free (SERF) comagnetometer achieves ultrahigh sensitivity, further improvements require suppressing technical noise and surpassing standard quantum limit. In this work, we develop a K-Rb-

^{21}

Ne SERF atomic comagnetometer that dynamically polarizes the electron and nuclear spins, shielding signals from direct interference by pump light. We establish a three-phase evolutionary model for hybrid spin ensemble dynamics, yielding a complete analytical solution, and analyze the responses to various spin perturbations. Additionally, we achieve an averaged 38.5

\%

suppression of the polarization noise and identify the key factors that limit sensitivity improvements. The dynamically polarized comagnetometer exhibits effective suppression of technical noise and holds the potential to overcome quantum noise limit, while offering promising applications in exploring new physics and precise magnetic field measurements.