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arXiv:2212.00401 · Physical Review A

Spin-noise spectroscopy of optical light shifts

J. Delpy, S. Liu, Pascal Neveu, E Wu, Fabien Bretenaker, Fabienne Goldfarb

Published Jan 5, 2023• 8 citations
arXivHTMLPDF

Abstract

A light-induced nonequilibrium regime is introduced in the standard spin noise spectroscopy, in which the laser light plays the role of both the probe beam and a driving field. The effect of the induced coherences is experimentally and theoretically demonstrated to be a splitting in the spin noise spectrum, which originates from and allows for the measurement of light shifts experienced by the atomic levels.

DOI
10.1103/physreva.107.l011701

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A light-induced nonequilibrium regime is introduced in the standard spin noise spectroscopy, in which the laser light plays the role of both the probe beam and a driving field. The effect of the induced coherences is experimentally and theoretically demonstrated to be a splitting in the spin noise spectrum, which originates from and allows for the measurement of light shifts experienced by the atomic levels.
Spectroscopy of atomic spin noise allows the determination of many sample properties such as energy-level structures and transverse-spin relaxation rates without the need to drive the system away from equilibrium with applied fields. Analysis of noise measurements can also reveal the processes that limit the sensitivity of a measured signal. Standard methods for spectroscopic noise measurements in atomic vapors rely on far-off-resonant optical probing. We present a method for investigating spin noise with a probe beam frequency relatively close to resonance and show how the back action of the probe on the atomic state can be subtracted from the recorded noise spectra. We verify this method experimentally by showing noise data that scale with the square root of the number of atoms, after the probe back action has been properly subtracted.
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.
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.
Spin noise spectroscopy (SNS) allows optically detect the fluctuations of a spin ensemble. Such fluctuations induce noise in the birefringence of the medium, which can be probed by recording polarization fluctuations of a laser beam after its propagation through the sample. As spin fluctuations are centered on the zero frequency, a transverse magnetic field is applied: spin precession then shifts the spin noise resonance at the Larmor frequency, so that it is not hidden by technical noises. The first SNS experiment was reported in the early 1980s by Alexandrov and Zapasskii, but it is only in 2004 that advances in narrow linewidth lasers and low noise electronics allow using this technique to probe various systems, such as thermal atomic vapors, semiconductors, or quantum wells. It was also proposed for magnetic field sensing, and possible measurements of correlations beyond the second-order raise a lot of interest, as they can give access to new quantum phenomena. We have performed spin noise spectroscopy in a metastable helium gas cell, and show that we can get two polarization dependent noise peaks when we record the linear instead of the circular birefringence fluctuations. Moreover, the relatively simple structure of helium allows us to show that it depends on the closest optical transition even when we are detuned by more than the Doppler broadening. We can also show that the behavior of the polarization dependence is strongly affected by time dependent B-field fluctuations. We performed simulations using a density matrix time evolution model, with added random fluctuations. It reproduces quite well the experimental results, including the transition dependence and the time dependent B-field noise effect, which have not been reported yet.
We studied the optical manipulation of spin coherence in rubidium atoms by using polarization spectroscopy with the pump-probe technique.Two types of optically induced spin echoes, namely on-and off-resonant manipulations, whose creation mechanism are the optical pumping effect and the light shift effect, respectively, are studied theoretically and experimentally.A theory of optically induced spin echoes that can be applied to both types of spin echoes is considered by using the density matrix, and a general expression for the refocusing efficiency of the control pulse is presented.The effect of the off-resonant manipulation was examined by using light pulses of two frequencies provided by two lasers.Vector models for the two types of spin echoes are presented, and the observed dependences of the frequency and the duration of the control pulse on the spin-echo intensity are suitably explained by the theoretically derived refocusing efficiency.The off-resonant manipulation gives the possibility of arbitrary-angle spin rotation around an arbitrary axis.
We studied the optical manipulation of spin coherence in rubidium atoms by using polarization spectroscopy with the pump-probe technique. Two types of optically induced spin echoes, namely on- and off-resonant manipulations, whose creation mechanism are the optical pumping effect and the light shift effect, respectively, are studied theoretically and experimentally. A theory of optically induced spin echoes that can be applied to both types of spin echoes is considered by using the density matrix, and a general expression for the refocusing efficiency of the control pulse is presented. The effect of the off-resonant manipulation was examined by using light pulses of two frequencies provided by two lasers. Vector models for the two types of spin echoes are presented, and the observed dependences of the frequency and the duration of the control pulse on the spin-echo intensity are suitably explained by the theoretically derived refocusing efficiency. The off-resonant manipulation gives the possibility of arbitrary-angle spin rotation around an arbitrary axis.