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arXiv:2605.31262 · Physical Review Research

Non-linear density scaling of spin noise reveals atomic correlations in warm vapors

Joseph Delpy, Elwyn Cardoz, Adwaith KV, Nikos Fayard, Nadia Belabas, Fabien bretenaker, Fabienne Goldfarb

quant-phSubmitted May 29, 2026• Announced Jun 1, 2026• 0 citations
arXivHTMLPDF

Abstract

We experimentally demonstrate a non-linear dependence of the spin noise variance on atomic density in a warm alkali vapor. Implementing high-bandwidth spin noise spectroscopy (SNS) near the D2 transition of rubidium, a quadratic spin noise contribution is shown to arise at high densities, in contrast with the linear dependence valid in non-interacting ensembles. This non-linear scaling is shown to crucially depend on the residual optical excitation of the vapor by the probe beam, suggesting it stems from atomic cross-correlations due to resonant dipole-dipole interaction (DDI) in the vapor. We support this claim by introducing an additional experimental protocol to quench the ddi, resulting in a suppression of both the quadratic scaling of the spin variance and the distortions of the spin noise spectrum induced by the interaction. These results extend the applications of SNS to the characterization of many-body correlations in complex quantum systems.

DOI
10.1103/dy7y-qllc
Comments
12 pages, 3 appendix sections, 10 figures

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We experimentally demonstrate a non-linear dependence of the spin noise variance on atomic density in a warm alkali vapor. Implementing high-bandwidth spin noise spectroscopy (SNS) near the D2 transition of rubidium, a quadratic spin noise contribution is shown to arise at high densities, in contrast with the linear dependence valid in non-interacting ensembles. This non-linear scaling is shown to crucially depend on the residual optical excitation of the vapor by the probe beam, suggesting it stems from atomic cross-correlations due to resonant dipole-dipole interaction (DDI) in the vapor. We support this claim by introducing an additional experimental protocol to quench the ddi, resulting in a suppression of both the quadratic scaling of the spin variance and the distortions of the spin noise spectrum induced by the interaction. These results extend the applications of SNS to the characterization of many-body correlations in complex quantum systems.
Spin noise spectroscopy (SNS) has become a mainstream approach to probe the dynamics of a spin ensemble in and out of equilibrium. Current models describing spin noise in interacting samples are based on an effective single-particle dynamics in a bath. Here, we report the observation of a strong interaction regime which significantly affects the spin dynamics. Performing SNS in a dense rubidium vapor, we observe anomalous distortions of the usual spin noise spectra, which we attribute to resonant dipole-dipole interaction within the ensemble. As the density of the vapor increases, we observe a dramatic broadening of the usual resonances and the emergence of an unexpected extra low-frequency noise component. We use a simple microscopic two-body numerical model to reproduce and discuss these observations. Our results suggest that the spectra cannot be described by the usual models of single-atom dynamics and arise from the evolution of interacting pairs of atoms. This work opens the way to the study of many-body spin noise or higher-order correlators in atomic vapors using SNS.
We report anomalous features in the spin noise spectroscopy (SNS) of a thin cell of a dense vapor of alkali atoms. At high densities and close to resonance, we observe a dramatic broadening of the spin noise spectra as well as an unexpected extra low-frequency noise component. With the help of a two-body model and simulations, we show that these features are the hallmark of a strong, long-range dipole-dipole interaction within the ensemble. The additional low-frequency noise reveals the correlated evolution of pair of atoms beyond the impact approximation. In this regime, we demonstrate that spin noise can no longer be obtained from one-body dynamics, opening the way for the characterization of many-body spin noise, atomic entanglement or higher order spin correlators in atomic vapors using SNS.
We describe a relatively non-invasive optical spectroscopy technique, known as spin noise spectroscopy (SNS), to probe spontaneous magnetization fluctuations in an alkali atomic vapor at thermal equilibrium. The atomic magnetization at a non-zero temperature fluctuates about its equilibrium value, and such magnetization (spin) noise imparts fluctuation in the measured Faraday rotation of a far-detuned, linearly polarized probe laser beam passing through the vapor. This Faraday rotation fluctuation reveals the intrinsic spin dynamics of the electrons in the alkali vapor. We present a systematic experimental study of the SNS realized in thermal rubidium vapor and illustrate how one can measure various magnetic and chemical properties of the sample with minimal perturbation. We also demonstrate the applicability of this spectroscopy technique in measuring the spin populations and their dynamics in different hyperfine and magnetic levels by optically pumping the atomic system.
We explore the applications of spin noise spectroscopy (SNS) for detection of the spin properties of atomic ensembles in and out of equilibrium. In SNS, a linearly polarized far-detuned probe beam on passing through an ensemble of atomic spins acquires the information of the spin correlations of the system which is extracted using its time-resolved Faraday-rotation noise. We measure various atomic, magnetic and sub-atomic properties as well as perform precision magnetometry using SNS in rubidium atomic vapor in thermal equilibrium. Thereafter, we manipulate the relative spin populations between different ground state hyperfine levels of rubidium by controlled optical pumping which drives the system out of equilibrium. We then apply SNS to probe such spin imbalance non-perturbatively. We further use this driven atomic vapor to demonstrate that SNS can have better resolution than typical absorption spectroscopy in detecting spectral lines in the presence of various spectral broadening mechanisms.
Abstract Optical quantum sensors based on alkali-metal atoms enable highly sensitive magnetic-field measurements in warm vapor. Their performance can become limited by intrinsic spin noise once technical noise sources are sufficiently suppressed. Characterizing temporal spin correlations is therefore important both for optimizing sensor sensitivity and for investigating quantum-enhanced sensing protocols. Here we investigate correlated spin fluctuations in a radio-frequency optical quantum sensor based on a high-density potassium vapor cell using pulsed probe readout. Orthogonal pump and probe beams establish and detect the spin polarization, while a bias magnetic field defines the sensing frequency and the probe pulses are synchronized electronically with the driven spin response. The protocol combines periodic probing, phase cycling, and variable-delay window subtraction. Phase cycling suppresses reproducible probe-induced coherent transients between experimental cycles, whereas window subtraction probes correlations between two measurements within the same cycle. The measured difference noise increases toward an asymptotic value with delay, demonstrating temporal correlations in the processed signal. This behavior is compatible with correlations expected from a conditional quantum non-demolition mechanism, but the present experiment does not independently establish spin squeezing below the standard quantum limit or uniquely exclude residual technical correlations. The protocol provides a practical framework for studying correlated noise in warm-vapor radio-frequency optical quantum sensors.