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Physical Review A

Spin-noise spectroscopy of a spin-one system

S. Liu, Pascal Neveu, J. Delpy, E Wu, Fabien Bretenaker, Fabienne Goldfarb

Published Feb 28, 2023• 9 citations
Publisher

Abstract

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 $^{4}\mathrm{He}$ at room temperature.

DOI
10.1103/physreva.107.023527

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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.
Abstract We perform spin noise spectroscopy experiments in metastable helium atoms at room temperature, with a probe light whose frequency is blue detuned from the D 0 line. Both circular birefringence fluctuations (Faraday noise) and linear birefringence fluctuations (ellipticity noise) are explored theoretically and experimentally. In particular, it is shown that in both cases but for different optical detunings, two noise resonances are isolated at the Larmor frequency and at twice the Larmor frequency with a behavior, which strongly depends on the orientation of the probe field polarization. The simple structure of metastable helium allows us to probe, model and explain the changes in the behavior of these peaks in terms of circular and linear dichroisms and birefringences as well as in terms of spin oscillation modes.
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 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.
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.
Highly sensitive Faraday rotation spectroscopy is used to measure the fluctuating magnetization noise of noninteracting rubidium atoms under resonant and nonresonant optical probing conditions. The spin-noise frequency spectra, in conjunction with the probe light detuning with respect to the D2{D}_{2}D2​ transition, reveal clear signatures of coherent coupling of the participating electronic levels. The results are explained by extended Bloch equations, including homogeneous and inhomogeneous broadening mechanisms. Our measurements further indicate that spin noise originating from excited states is governed at high intensities by collective effects.
We investigate theoretically and experimentally fluctuations of high spin (F>12F\phantom{\rule{0.16em}{0ex}}>\phantom{\rule{0.16em}{0ex}}\frac{1}{2}F>21​) beyond the linear response regime and demonstrate dramatic modifications of the spin noise spectra in the high power density probe field. Several effects related to an interplay of high spin and perturbation are predicted theoretically and revealed experimentally, including strong sensitivity of the spin noise spectra to the mutual orientation of the probe polarization plane and magnetic field direction, appearance of high harmonics of the Larmor frequency in the spin noise, and the fine structure of the Larmor peaks. We demonstrate the ability of spin noise spectroscopy to access the nonlinear effects related to the renormalization of the spin states by strong electromagnetic fields.