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arXiv:1709.07959 · Physical Review A

Homogenization of Doppler broadening in spin-noise spectroscopy

M. Yu. Petrov, I. I. Ryzhov, Dmitry S. Smirnov, Leonid Yu. Beliaev, R. A. Potekhin, Михаил Михайлович Глазов, V. N. Kulyasov, G. G. Kozlov, Evgenii B. Aleksandrov, Valerii S Zapasskii

Published Mar 5, 2018• 12 citations
arXivHTMLPDF

Abstract

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 $D{}_{2}$ 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.

DOI
10.1103/physreva.97.032502

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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.
We study the optical spin noise spectra of Rb atomic gas with different broadening mechanisms. The first is homogeneous broadening using 250 Torr nitrogen buffer gas, while the other mechanism is inhomogeneous broadening via the Doppler effect without buffer gas. Spin noise signals are measured by the typical spin noise spectroscopy geometry (single-pass geometry) and the saturated absorption spectroscopy geometry (double-pass geometry). In the homogeneously broadened system, the line shape of the optical spin noise spectra shows a pronounced dip that vanishes at the center of the band in both geometries. In the inhomogeneously broadened system, however, a peak in the single-pass geometry and a dip in the double-pass geometry at the band center are observed. The difference between the optical spin noise spectra from these two systems arises from their different level-broadening mechanisms.
Spontaneous fluctuations of the magnetization of a spin system in thermodynamic equilibrium (spin noise) manifest themselves as noise in the Faraday rotation of probe light. We show that the correlation properties of this noise over the optical spectrum can provide clear information about the composition of the spin system that is largely inaccessible for conventional linear optics. Such optical spectroscopy of spin noise, e.g., allows us to clearly distinguish between optical transitions associated with different spin subsystems, to resolve optical transitions that are unresolvable in the usual optical spectra, to unambiguously distinguish between homogeneously and inhomogeneously broadened optical bands, and to evaluate the degree of inhomogeneous broadening. These new possibilities are illustrated by theoretical calculations and by experiments on paramagnets with different degrees of inhomogeneous broadening of optical transitions [atomic vapors of 41K and singly charged (In,Ga)As quantum dots].
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.
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.
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.
We uncover a highly nontrivial dependence of the spin-noise (SN) resonance broadening induced by the intense probe beam. The measurements were performed by probing the cell with cesium vapor at the wavelengths of the transition $6^{2}S_{1/2}\ensuremath{\leftrightarrow}6^{2}P_{3/2}$ (D2{D}_{2}D2​ line) with the unresolved hyperfine structure of the excited state. The light-induced broadening of the SN resonance was found to differ strongly at different slopes of the D2{D}_{2}D2​ line and, generally, varied nonmonotonically with light power. We discuss the effect in terms of the phenomenological Bloch equations for the spin fluctuations and demonstrate that the SN broadening behavior strongly depends on the relation between the pumping and excited-level decay rates, the spin precession, and decoherence rates. To reconcile the puzzling experimental results, we propose that the degree of optical perturbation of the spin system is controlled by the route of the excited-state relaxation of the atom or, in other words, that the act of optical excitation of the atom does not necessarily break down completely its ground-state coherence and continuity of the spin precession. Spectral asymmetry of the effect, in this case, is provided by the position of the ``closed'' transition $F=4\ensuremath{\leftrightarrow}{F}^{\ensuremath{'}}=5$ at the short-wavelength side of the line. This hypothesis, however, remains to be proven by microscopic calculations.