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arXiv:1709.07360 · Physical Review A

Spin-noise spectroscopy of randomly moving spins in the model of light scattering: Two-beam arrangement

G. G. Kozlov, I. I. Ryzhov, Valerii S Zapasskii

Published Jan 29, 2018• 14 citations
arXivHTMLPDF

Abstract

A strict analytical solution of the problem of spin-noise signal formation in a volume medium with randomly moving spin carriers is presented. The treatment is carried out in the model of light scattering in a medium with fluctuating inhomogeneity. Along with conventional single-beam geometry, we consider the two-beam arrangement, with the scattering field of the auxiliary (tilted) beam heterodyned on the photodetector illuminated by the main beam. It is shown that the spin-noise signal detected in the two-beam arrangement is highly sensitive to motion (diffusion) of the spin carriers within the illuminated volume and thus can provide additional information about the spin dynamics and spatial correlations of spin polarization in the volume media. Our quantitative estimates show that, under real experimental conditions, spin diffusion may strongly suppress the spin-noise signal in the two-beam geometry. The mechanism of this suppression is similar to that of the time-of-flight broadening with the critical distance determined by the period of two-beam spatial interference rather than by the beam diameter.

DOI
10.1103/physreva.97.013848

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A strict analytical solution of the problem of spin-noise signal formation in a volume medium with randomly moving spin carriers is presented. The treatment is carried out in the model of light scattering in a medium with fluctuating inhomogeneity. Along with conventional single-beam geometry, we consider the two-beam arrangement, with the scattering field of the auxiliary (tilted) beam heterodyned on the photodetector illuminated by the main beam. It is shown that the spin-noise signal detected in the two-beam arrangement is highly sensitive to motion (diffusion) of the spin carriers within the illuminated volume and thus can provide additional information about the spin dynamics and spatial correlations of spin polarization in the volume media. Our quantitative estimates show that, under real experimental conditions, spin diffusion may strongly suppress the spin-noise signal in the two-beam geometry. The mechanism of this suppression is similar to that of the time-of-flight broadening with the critical distance determined by the period of two-beam spatial interference rather than by the beam diameter.
The spin-noise signal in the Faraday-rotation-based detection technique can be considered equally correctly either as a manifestation of the spin-flip Raman effect or as a result of light scattering in the medium with fluctuating gyrotropy. In this paper, we present rigorous description of the signal formation process upon heterodyning of the field scattered due to fluctuating gyrotropy. Along with conventional single-beam experimental arrangement, we consider here a more complicated, but more informative, two-beam configuration that implies the use of an auxiliary light beam passing through the same scattering volume and delivering additional scattered light to the detector. We show that the signal in the spin-noise spectroscopy (SNS) arising due to heterodyning of the scattered field is formed only by the scattered field components the wave vectors of which coincide with those of the probe field. Therefore, in principle, the detected signal in SNS can be increased by increasing overlap of the two fields in the momentum space. We also show that, in the two-beam geometry of SNS, contribution of the auxiliary (tilted) beam to the detected signal is produced only by the region of overlap between the two beams in real space and can be expressed analytically as the Fourier transform of the spatial correlation function of the gyrotropy at the difference of their wave vectors. These features of the two-beam geometry can be used for tomographic measurements in spin systems (a more sophisticated version of three-dimensional tomography proposed earlier) and for studying spatial spin correlations by means of noise spectroscopy.
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.
It is known that linear birefringence of the medium essentially hinders measuring the Faraday effect. For this reason, optically anisotropic materials have never been considered as objects of the Faraday-rotation-based spin noise spectroscopy (SNS). We show, both theoretically and experimentally, that strong optical anisotropy that may badly suppress the regular Faraday rotation of the medium, practically does not affect the measurement of the spatially uncorrelated spin fluctuations. An important consequence of this result is that the Faraday-rotation noise should be also insensitive to spatially nonuniform birefringence, which makes the SNS applicable to a wide class of optically anisotropic and inhomogeneous materials. We also show that the birefringent media provide additional opportunity to measure spatial spin correlations. Results of the experimental measurements of the spin-noise spectra performed on 4fff--4fff transitions of Nd3+^{3+}3+ ions in the CaWO4_44​ and LiYF4_44​ crystals well agree with the theory.
The spin-noise spectroscopy, being a nonperturbative linear optics tool, is still reputed to reveal a number of capabilities specific to nonlinear optics techniques. The effect of the Doppler broadening homogenization discovered in this work essentially widens these unique properties of spin-noise spectroscopy. We investigate spin noise of a classical system---cesium atoms vapor with admixture of buffer gas---by measuring the spin-induced Faraday rotation fluctuations in the region of D2D{}_{2}D2​ line. The line, under our experimental conditions, is strongly inhomogeneously broadened due to the Doppler effect. Despite that, optical spectrum of the spin-noise power has the shape typical for the homogeneously broadened line with a dip at the line center. This fact is in stark contrast with the results of previous studies of inhomogeneous quantum dot ensembles and Doppler broadened atomic systems. In addition, the two-color spin-noise measurements have shown, in a highly spectacular way, that fluctuations of the Faraday rotation within the line are either correlated or anticorrelated depending on whether the two wavelengths lie on the same side or on different sides of the resonance. The experimental data are interpreted in the frame of the developed theoretical model which takes into account both kinetics and spin dynamics of Cs atoms. It is shown that the unexpected behavior of the Faraday rotation noise spectra and effective homogenization of the optical transition in the spin-noise measurements are related to smallness of the momentum relaxation time of the atoms as compared with their spin-relaxation time. Our findings demonstrate abilities of spin-noise spectroscopy for studying dynamic properties of inhomogeneously broadened ensembles of randomly moving spins.
Spin noise spectroscopy (SNS) is a new method for studying magnetic resonance and spin dynamics that has gained, in the last several years, a considerable popularity. The method is based on measuring magnetization noise of a paramagnet using the Faraday rotation technique. In strong contrast with methods of nonlinear optics, the spectroscopy of spin noise is considered to be essentially nonperturbative. At the same time, presently, it became clear that the SNS, as an optical technique, demonstrates abilities lying far beyond the bounds of conventional linear optics. Specifically, the SNS allows one to penetrate inside an inhomogeneously broadened absorption band and to determine its homogeneous width, to realize a sort of pump-probe spectroscopy without any optical nonlinearity, to probe a bulk inhomogeneous medium by focal point of a probe beam, etc. This may seem especially puzzling when taken into account that SNS can be considered just as a version of Raman spectroscopy, which is known to be deprived of such abilities. Understanding of these paradoxical features of SNS technique is required for the present-day applications of SNS and its further development. In this paper, we present a general analysis of this apparent inconsistency from the viewpoint of distinction between spectroscopy of the light intensity and of the light field and provide its resolution.