Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1701.04268 · Physical Review A

Light scattering in a medium with fluctuating gyrotropy: Application to spin-noise spectroscopy

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

Published Apr 10, 2017• 13 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.95.043810

Related papers

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

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.

arXiv:1709.07360•Physical Review A•Jan 29, 2018•14 citations

Optical spin noise spectroscopy: application for study of gyrotropy spatial correlations

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

The single scattering theory is applied to spin noise spectroscopy (SNS). The case of two Gaussian probe beams tilted with respect to each other is analysed. It is shown that SNS signal in this case carry information about spatial correlations of studied gyrotropic medium.

arXiv:1611.02080•Nov 7, 2016•0 citations

Raman scattering model of the spin noise

G. G. Kozlov, A. A. Fomin, M. Yu. Petrov +2 more

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.

arXiv:2102.00947•Optics Express•Jan 18, 2021•7 citations

Linear optics, Raman scattering, and spin noise spectroscopy

Михаил Михайлович Глазов, Valerii S Zapasskii

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.

arXiv:1502.01155•Optics Express•Apr 24, 2015•35 citations

Spin noise in birefringent and inhomogeneous media

V. O. Kozlov, Н. С. Кузнецов, Dmitry S. Smirnov +3 more

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 4$f$--4$f$ transitions of Nd$^{3+}$ ions in the CaWO$_4$ and LiYF$_4$ crystals well agree with the theory.

arXiv:2201.09775•Jan 24, 2022•0 citations

Creation and dynamics of spin fluctuations in a noisy magnetic field

J. Delpy, Shengchi Liu, Pascal Neveu +4 more

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.

arXiv:2309.02916•New Journal of Physics•Sep 1, 2023•4 citations
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.
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 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.
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.
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.
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.