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Scientific Reports

Optical spin noise spectra of Rb atomic gas with homogeneous and inhomogeneous broadening

Jian Ma, Ping Shi, Xuan Qian, Yaxuan Shang, Yang Ji

Published Aug 25, 2017• 10 citations
Publisher

Abstract

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.

DOI
10.1038/s41598-017-08759-4

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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.
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.
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].
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.
Polarization and Rayleigh type optical mixing spectra of a homogeneously and inhomogeneously broadened two-level system are calculated. We show that the nonlinear signal has contributions from the population pulsation and saturation effect. In the homogeneous system these effects can induce an asymmetric spectrum when the probe frequency is different from the resonant value. In the inhomogeneous system the spectral response is always symmetric independent of the probe frequency value. Line saturation and dynamic stark splitting are substantially reduced in the inhomogeneous case. The mentioned differences can be used to identify the type of broadening of a given spectral line.
We explore the applications of spin noise spectroscopy (SNS) for detection of the spin properties of atomic ensembles in and out of equilibrium. In SNS, a linearly polarized far-detuned probe beam on passing through an ensemble of atomic spins acquires the information of the spin correlations of the system which is extracted using its time-resolved Faraday-rotation noise. We measure various atomic, magnetic and sub-atomic properties as well as perform precision magnetometry using SNS in rubidium atomic vapor in thermal equilibrium. Thereafter, we manipulate the relative spin populations between different ground state hyperfine levels of rubidium by controlled optical pumping which drives the system out of equilibrium. We then apply SNS to probe such spin imbalance non-perturbatively. We further use this driven atomic vapor to demonstrate that SNS can have better resolution than typical absorption spectroscopy in detecting spectral lines in the presence of various spectral broadening mechanisms.