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arXiv:1108.0591 · Physical Review A

Spin-noise spectroscopy under resonant optical probing conditions: Coherent and nonlinear effects

H. Horn, Georg M. Müller, Ernst Maria Rasel, Luis Santos, J. Hübner, M. Oestreich

Published Oct 31, 2011• 27 citations
arXivHTMLPDF

Abstract

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 ${D}_{2}$ 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.

DOI
10.1103/physreva.84.043851

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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.
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].
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 describe a relatively non-invasive optical spectroscopy technique, known as spin noise spectroscopy (SNS), to probe spontaneous magnetization fluctuations in an alkali atomic vapor at thermal equilibrium. The atomic magnetization at a non-zero temperature fluctuates about its equilibrium value, and such magnetization (spin) noise imparts fluctuation in the measured Faraday rotation of a far-detuned, linearly polarized probe laser beam passing through the vapor. This Faraday rotation fluctuation reveals the intrinsic spin dynamics of the electrons in the alkali vapor. We present a systematic experimental study of the SNS realized in thermal rubidium vapor and illustrate how one can measure various magnetic and chemical properties of the sample with minimal perturbation. We also demonstrate the applicability of this spectroscopy technique in measuring the spin populations and their dynamics in different hyperfine and magnetic levels by optically pumping the atomic system.
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.
We develop a theory of spin-noise spectroscopy of itinerant, noninteracting, and spin-carrying fermions in different regimes of temperature and disorder. We use kinetic equations for the density matrix in spin variables. We find a general result with a clear physical interpretation, and discuss its dependence on temperature, the size of the system, and applied magnetic field. We consider two classes of experimental probes: (1) electron-spin-resonance-type measurements, in which the probe response to a uniform magnetization increases linearly with the volume sampled and (2) optical Kerr/Faraday rotation-type measurements, in which the probe response to a uniform magnetization increases linearly with the length of the light propagation in the sample but is independent of the cross section of the light beam. Our theory provides a framework for interpreting recent experiments on atomic gases and conduction electrons in semiconductors and provides a baseline for identifying the effects of interactions on spin-noise spectroscopy.