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arXiv:2102.00938 · Physical Review A

Nonlinear spectroscopy of high-spin fluctuations

Anatoly A. Fomin, M. Yu. Petrov, I. I. Ryzhov, G. G. Kozlov, Valerii S Zapasskii, Михаил Михайлович Глазов

Published Feb 10, 2021• 8 citations
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Abstract

We investigate theoretically and experimentally fluctuations of high spin ($F\phantom{\rule{0.16em}{0ex}}>\phantom{\rule{0.16em}{0ex}}\frac{1}{2}$) 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.

DOI
10.1103/physreva.103.023104

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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.
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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.
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 attract attention to the fact that the ultimate (shot-noise-limited) polarimetric sensitivity can be enhanced by orders of magnitude leaving the photon flux incident onto the photodetector on the same low level. This opportunity is of crucial importance for present-day spin noise spectroscopy, where a direct increase of sensitivity by increasing the probe beam power is strongly restricted by the admissible input power of the broadband photodetectors. The gain in sensitivity is achieved by replacing the 45${}^{\ensuremath{\circ}}$ polarization geometry commonly used in conventional schemes with balanced detectors by geometries with stronger polarization extinction. The efficiency of these high-extinction polarization geometries with enhancement of the detected signal by more than an order of magnitude is demonstrated by measurements of the spin noise spectra of bulk nnn:GaAs in the spectral range 835--918 nm. It is shown that the inevitable growth of the probe beam power with the sensitivity gain makes spin noise spectroscopy much more perturbative, but, at the same time, opens up fresh opportunities for studying nonlinear interactions of strong light fields with spin ensembles.
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.
Optically pumped magnetometers (OPMs) are revolutionizing the task of magnetic-field sensing due to their extremely high sensitivity combined with technological improvements in miniaturization which have led to compact and portable devices. OPMs can be based on spin-oriented or spin-aligned atomic ensembles which are spin polarized through optical pumping with circular or linear polarized light, respectively. Characterization of OPMs and the dynamical properties of their noise is important for applications in real-time sensing tasks. In our work, we experimentally perform spin noise spectroscopy of an alignment-based magnetometer. Moreover, we propose a stochastic model that predicts the noise power spectra exhibited by the device when, apart from the strong magnetic field responsible for the Larmor precession of the spin, white noise is applied in the perpendicular direction aligned with the pumping-probing beam. By varying the strength of the noise applied as well as the linear-polarization angle of incoming light, we verify the model to accurately predict the heights of the Larmor-induced spectral peaks and their corresponding linewidths. Our work paves the way for alignment-based magnetometers to become operational in real-time sensing tasks. Published by the American Physical Society 2024