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arXiv:2204.08748 · Physical Review A

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

K. Mouloudakis, Georgios Vasilakis, Vito Giovanni Lucivero, Jia Kong, Iannis K. Kominis, Morgan W. Mitchell

Published Aug 15, 2022• 25 citations
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Abstract

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.

DOI
10.1103/physreva.106.023112

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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.
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.
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.
We report an experimental and theoretical study of spin-noise correlations in a $^{87}\mathrm{Rb}\text{\ensuremath{-}}^{133}\mathrm{Cs}$ unpolarized alkali-metal vapor dominated by spin-exchange collisions. We observe strong unequal-time interspecies correlations and account for these with a first-principles theoretical model. Since the two atomic species have different spin precession frequencies, the dual-species vapor enables the use of an additional experimental handle, the applied magnetic field, for untangling various subtypes of spin correlations. In particular, the measured cross-correlation and autocorrelation spectra shed light on a number of spin-dynamic effects involving intra-atom, interatom, intraspecies, and interspecies correlations. Cross-correlation coefficients exceeding 6060%60 have been observed at low magnetic fields, where the two spin species couple strongly via spin-exchange collisions. The understanding of such spontaneously generated correlations can motivate the design of quantum-enhanced measurements with single or multispecies spin-polarized alkali-metal vapors used in quantum sensing applications.
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.
The authors perform spin-noise spectroscopy on an unpolarized 87{}^{87}87Rb vapor in the spin-exchange-relaxation-free regime and observe noise spectral distributions that deviate strongly from Lorentzian models that accurately describe lower-density regimes. This observation shows that new kinds of information can be extracted from noise spectra and may improve atomic vapor sensors.
We study the fundamental limits of noise spectroscopy using estimation theory, Faraday rotation probing of an atomic spin system, and squeezed light. We find a simple and general expression for the Fisher information, which quantifies the sensitivity to spectral parameters such as resonance frequency and linewidth. For optically detected spin noise spectroscopy, we find that shot noise imposes ``local'' standard quantum limits for any given probe power and atom number, and also ``global'' standard quantum limits when the probe power and atom number are taken as free parameters. We confirm these estimation theory results using nondestructive Faraday rotation probing of hot Rb vapor, observing the predicted optima, and finding good quantitative agreement with a first-principles calculation of the spin noise spectra. Finally, we show sensitivity beyond the atom- and photon-number-optimized global standard quantum limit using squeezed light.