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arXiv:2002.06035

Polarimetric observation of noise of linear birefringence of cesium atomic vapors spectrally localized at double Larmor frequency in a magnetic field

G. G. Kozlov, Anatoly A. Fomin, M. Yu. Petrov, Valerii S Zapasskii

Published Feb 14, 2020• 0 citations
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Abstract

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.

DOI
10.48550/arxiv.2002.06035

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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 αα 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 αα 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.
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.
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.
Nonlinear magneto-optical resonances occurring for near-zero magnetic field are studied in Rb vapor using light-noise spectroscopy. With a balanced detection polarimeter, we observe high contrast variations of the noise power (at fixed analysis frequency) carried by diode laser light resonant with the $5{\mathrm{S}}_{1∕2}\phantom{\rule{0.2em}{0ex}}(F=2)\ensuremath{\rightarrow}5{\mathrm{P}}_{1∕2}\phantom{\rule{0.2em}{0ex}}(F=1)$ transition 87Rb^{87}\mathrm{Rb}87Rb and transmitted through a rubidium vapor cell as a function of magnetic field BBB. A symmetric resonance doublet of anticorrelated noise is observed for orthogonal polarizations around B=0B=0B=0 as a manifestation of ground-state coherence. We also observe sideband noise resonances when the magnetic field produces an atomic Larmor precession at a frequency corresponding to one-half of the analysis frequency. The resonances on the light fluctuations are the consequence of phase to amplitude noise conversion owing to nonlinear coherence effects in the response of the atomic medium to the fluctuating field. A theoretical model (derived from linearized Bloch equations) is presented that reproduces the main qualitative features of the experimental signals under simple assumptions.
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.
We present an experimental study of the spectra produced by optical--radio-frequency double resonance in which resonant linearly polarized laser light is used in the optical pumping and detection processes. We show that the experimental spectra obtained for cesium are in excellent agreement with a very general theoretical model developed in our group [Weis, Bison, and Pazgalev, Phys. Rev. A 74, 033401 (2006)] and we investigate the limitations of this model. Finally, the results are discussed in view of their use in the study of relaxation processes in aligned alkali-metal vapors.
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.