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arXiv:2309.02916 · New Journal of Physics

Creation and dynamics of spin fluctuations in a noisy magnetic field

J. Delpy, Shengchi Liu, Pascal Neveu, C Roussy, Th. Jolicœur, Fabien Bretenaker, Fabienne Goldfarb

Published Sep 1, 2023• 4 citations
arXivHTMLPDF

Abstract

Abstract We theoretically and numerically investigate the spin fluctuations induced in a thermal atomic ensemble by an external fluctuating uniaxial magnetic field, in the context of a standard spin noise spectroscopy (SNS) experiment. We show that additional spin noise is excited, which dramatically depends on the magnetic noise variance and bandwidth, as well as on the power of the probe light and its polarization direction. We develop an analytical perturbative model proving that this spin noise first emerges from the residual optical pumping in the medium, which is then converted into spin fluctuations by the magnetic noise and eventually detected using SNS. The system studied is a spin-1 system, which thus shows both Faraday rotation and ellipticity noises induced by the random magnetic fluctuations. The analytical model gives results in perfect agreement with the numerical simulations, with potential applications in future experimental characterization of stray field properties and their influence on spin dynamics.

DOI
10.1088/1367-2630/acfb30

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Applied Physics Letters•Aug 24, 2026•0 citations
Abstract We theoretically and numerically investigate the spin fluctuations induced in a thermal atomic ensemble by an external fluctuating uniaxial magnetic field, in the context of a standard spin noise spectroscopy (SNS) experiment. We show that additional spin noise is excited, which dramatically depends on the magnetic noise variance and bandwidth, as well as on the power of the probe light and its polarization direction. We develop an analytical perturbative model proving that this spin noise first emerges from the residual optical pumping in the medium, which is then converted into spin fluctuations by the magnetic noise and eventually detected using SNS. The system studied is a spin-1 system, which thus shows both Faraday rotation and ellipticity noises induced by the random magnetic fluctuations. The analytical model gives results in perfect agreement with the numerical simulations, with potential applications in future experimental characterization of stray field properties and their influence on spin dynamics.
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.
Spin noise spectroscopy (SNS) allows optically detect the fluctuations of a spin ensemble. Such fluctuations induce noise in the birefringence of the medium, which can be probed by recording polarization fluctuations of a laser beam after its propagation through the sample. As spin fluctuations are centered on the zero frequency, a transverse magnetic field is applied: spin precession then shifts the spin noise resonance at the Larmor frequency, so that it is not hidden by technical noises. The first SNS experiment was reported in the early 1980s by Alexandrov and Zapasskii, but it is only in 2004 that advances in narrow linewidth lasers and low noise electronics allow using this technique to probe various systems, such as thermal atomic vapors, semiconductors, or quantum wells. It was also proposed for magnetic field sensing, and possible measurements of correlations beyond the second-order raise a lot of interest, as they can give access to new quantum phenomena. We have performed spin noise spectroscopy in a metastable helium gas cell, and show that we can get two polarization dependent noise peaks when we record the linear instead of the circular birefringence fluctuations. Moreover, the relatively simple structure of helium allows us to show that it depends on the closest optical transition even when we are detuned by more than the Doppler broadening. We can also show that the behavior of the polarization dependence is strongly affected by time dependent B-field fluctuations. We performed simulations using a density matrix time evolution model, with added random fluctuations. It reproduces quite well the experimental results, including the transition dependence and the time dependent B-field noise effect, which have not been reported yet.
The spin-noise mechanisms in a spin-1 system are theoretically and experimentally investigated in detail. Eight different independent spin degrees of freedom are isolated, leading to spin-noise signals at the Larmor frequency or its second harmonic in the presence of a magnetic field. The signatures of these different modes of the detuned probe light beam polarization fluctuations, observed either as Faraday rotation noise or as ellipticity noise, are shown to depend dramatically on the probed transition. In particular, depending on the Zeeman structure of the upper level of the transitions, the different noise modes can be visible or not, and their dependence on the probe polarization can be completely modified. Those predictions are successfully compared with measurements of spin-noise signals using three different transitions of an ensemble of metastable 4He^{4}\mathrm{He}4He at room temperature.
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.
The mechanism of formation of the polarimetric signal observed in the spin noise spectroscopy (SNS) is analyzed from the viewpoint of the light scattering theory. A rigorous calculation of the polarimetric signal (Faraday rotation or ellipticity) recorded in the SNS is presented in the approximation of single scattering. We show that it is most correctly to consider this noise as a result of scattering of the probe light beam by fluctuating susceptibility of the medium. Fluctuations of the gyrotropic (antisymmetric) part of the susceptibility tensor lead to appearance of the typical for the SNS Faraday rotation noise at the Larmor frequency. At the same time, fluctuations of linear anisotropy of the medium (symmetric part of the susceptibility tensor) give rise to the ellipticity noise of the probe beam spectrally localized at the double Larmor frequency. The results of the theoretical analysis well agree with the experimental data on the ellipticity noise in cesium vapor.
In atomic spin sensors based on optical pumping, pump beam instabilities can drive atomic spin polarization fluctuations, referred to here as pump-induced spin polarization noise, which may limit sensitivity and long-term stability. Because the local pump field inside the cell can differ from that inferred from external optical diagnostics, it remains difficult to directly quantify the actual in situ spin polarization noise and to evaluate and suppress its contribution to the sensor noise floor. Here, we propose an in situ decoupling method based on spin dynamics, in which a large longitudinal detuning field suppresses magnetic field and rotation responses, while a transverse projection field converts pump-induced fluctuations in longitudinal spin polarization into a measurable transverse spin signal. Demonstrated in a K-Rb-21Ne spin exchange relaxation free (SERF) comagnetometer, the proposed method suppresses the magnetic-field response by approximately 180-fold and enhances the pump-power-noise response by approximately 380-fold, thereby enabling effective separation and evaluation of pump-induced spin polarization noise. The method employs the atomic ensemble as an in situ probe of the spin dynamic response to the local pump optical field. It enables quantitative identification of pump fluctuation associated noise and direct evaluation of optical field stability under actual operating conditions, thereby providing an experimental basis for optical field stabilization and noise suppression assessment in SERF comagnetometers and related alkali atomic spin sensors.