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arXiv:2202.10896 · New Journal of Physics

Birefringence and dichroism effects in the spin noise spectra of a spin-1 system

Shengchi Liu, Pascal Neveu, J. Delpy, L. Hemmen, E. Brion, E Wu, Fabien Bretenaker, Fabienne Goldfarb

Published Nov 1, 2022• 9 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1088/1367-2630/aca428

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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 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 study radio-frequency spectrum of ellipticity noise of a probe laser beam transmitted through a cell with cesium vapor in a magnetic field. The experimental results are interpreted in terms of the model proposed by Gorbovitskii and Perel (Opt. Spektrosc. 54, 388 (1983)) according to which the observed noise arises due to heterodyning of the light scattered by fluctuations of the tensor $ α$ of optical susceptibility of cesium vapor. We show, both experimentally and theoretically, that, in the noise measurements if this kind, along with fluctuations of the antisymmetric (gyrotropic) part of the tensor $ α$ at the Larmor frequency, may be observed fluctuations of its symmetric part, corresponding to fluctuations of linear birefringence (alignment) of the atomic system. The polarization noise provided by these fluctuations is localized spectrally at the double Larmor frequency.
Two precessing spins that are parallel (`oriented') or antiparallel (`aligned') modulate the probe light beam at the precession or double-precession frequency, respectively. Stochastic modulation of light by a spin-system at Larmor frequency is the noise of spin orientation detected in conventional spin noise spectroscopy. Polarization modulation of the probe beam at the double Larmor frequency discovered by the authors in experiments with cesium atoms is ascribed to fluctuations of spin alignment. While the spin-orientation noise is revealed as the noise of gyrotropy, the spin-alignment noise is observed in the fluctuations of linear birefringence.
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.
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.