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.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:2201.09775Jan 24, 20220 citations

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

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

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 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.

arXiv:1701.04268Physical Review AApr 10, 201713 citations

Spin Noise Spectroscopy: Three Plots

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

The effect of magnetic resonance in the Faraday-rotation noise, demonstrated for the first time on an atom system more than 40 years ago, laid the foundations of a new research direction, the spin noise spectroscopy, that has been developing extensively in the last 20 years. Currently, the most popular research objects are atom and semiconductor paramagnetic materials, while research subjects are the magnetic resonance spectroscopy, the spin dynamics, the optical spectroscopy, the spectroscopy of light polarization noises. The rapid development of this new research direction laying at the interface between optics and radio spectroscopy continuously extends the field of its applicability and opens new opportunities to use it in the experimental physics. In this article we present a few episodes that are important stages in the spin noise spectroscopy development in the last years. The article was prepared as a report on the XV Russian Conference on the Physics of Semiconductors. Keywords: spin noise spectroscopy, magnetic resonance, optical anisotropy, inhomogeneous broadening.The effect of magnetic resonance in the Faraday-rotation noise, demonstrated for the first time on an atom system more than 40 years ago, laid the foundations of a new research direction, the spin noise spectroscopy, that has been developing extensively in the last 20 years. Currently, the most popular research objects are atom and semiconductor paramagnetic materials, while research subjects are the magnetic resonance spectroscopy, the spin dynamics, the optical spectroscopy, the spectroscopy of light polarization noises. The rapid development of this new research direction laying at the interface between optics and radio spectroscopy continuously extends the field of its applicability and opens new opportunities to use it in the experimental physics. In this article we present a few episodes that are important stages in the spin noise spectroscopy development in the last years. The article was prepared as a report on the XV Russian Conference on the Physics of Semiconductors. Keywords: spin noise spectroscopy, magnetic resonance, optical anisotropy, inhomogeneous broadening.

Оптика и спектроскопияJan 1, 20220 citations

Nonlinear Faraday effect and spin noise in rare-earth activated crystals

A. N. Kamenskii, E. I. Baibekov, Malkin Boris Zalmanovich +4 more

The spin-noise spectroscopy (SNS) method implies high efficiency of conversion of the spin-system magnetization to the Faraday rotation angle. Generally, this efficiency cannot be estimated using the characteristics of the regular magnetooptical activity of a paramagnet. However, it may be drastically enhanced in systems with strong inhomogeneous broadening of the optical transitions. This enhancement leads to the giant spin-noise gain effect and previously allowed one to apply the SNS to rare-earth activated crystals. We show that the nonlinear resonant Faraday effect can be used to measure the homogeneous width of the inhomogeneously broadened transition and, thus, to estimate the applicability of the SNS to this type of paramagnet. We present the theoretical description of the effect and perform measurements on intraconfigurational ($4f\text{\ensuremath{-}}4f$) transitions of the trivalent rare-earth ions of neodymium and ytterbium in fluorite-based crystals. The proposed experimental approach establishes new links between the effects of nonlinear optics and spin-noise characteristics of crystals with paramagnetic impurities and offers new methods of research in the physics of impurity crystals.The spin-noise spectroscopy (SNS) method implies high efficiency of conversion of the spin-system magnetization to the Faraday rotation angle. Generally, this efficiency cannot be estimated using the characteristics of the regular magnetooptical activity of a paramagnet. However, it may be drastically enhanced in systems with strong inhomogeneous broadening of the optical transitions. This enhancement leads to the giant spin-noise gain effect and previously allowed one to apply the SNS to rare-earth activated crystals. We show that the nonlinear resonant Faraday effect can be used to measure the homogeneous width of the inhomogeneously broadened transition and, thus, to estimate the applicability of the SNS to this type of paramagnet. We present the theoretical description of the effect and perform measurements on intraconfigurational ($4f\text{\ensuremath{-}}4f$) transitions of the trivalent rare-earth ions of neodymium and ytterbium in fluorite-based crystals. The proposed experimental approach establishes new links between the effects of nonlinear optics and spin-noise characteristics of crystals with paramagnetic impurities and offers new methods of research in the physics of impurity crystals.

arXiv:2111.01707Physical review. B./Physical review. BNov 22, 20212 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.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:2102.00947Optics ExpressJan 18, 20217 citations

Polarized light in an anisotropic medium versus spin in a magnetic field

Valerii S Zapasskii, G. G. Kozlov

The analogy between polarization optics effects and the dynamics of a spin in a magnetic field is analyzed based on the fact that the Bloch equation for a spin in a magnetic field is formally identical to the evolution equation for the quasi-spin vector of a light propagating in an optically anisotropic medium. Among the effects discussed within this framework are light polarization beats in a birefringent medium; optical activity suppression in the media with linear birefringence; suppression of linear birefringence in the media with spatially modulated gyration; 'adiabatic' transformation of light polarization in media of smoothly varying anisotropy, and two- and three-pulse polarization echoes.The analogy between polarization optics effects and the dynamics of a spin in a magnetic field is analyzed based on the fact that the Bloch equation for a spin in a magnetic field is formally identical to the evolution equation for the quasi-spin vector of a light propagating in an optically anisotropic medium. Among the effects discussed within this framework are light polarization beats in a birefringent medium; optical activity suppression in the media with linear birefringence; suppression of linear birefringence in the media with spatially modulated gyration; 'adiabatic' transformation of light polarization in media of smoothly varying anisotropy, and two- and three-pulse polarization echoes.

Physics-UspekhiAug 31, 199920 citations

f

--4

f

transitions of Nd

^{3+}

ions in the CaWO

_4

and LiYF

_4

crystals well agree with the theory.