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arXiv:1407.2895 · Physical Review Letters

Spin Noise Spectroscopy Beyond Thermal Equilibrium and Linear Response

Ph. Glasenapp, Nikolai A. Sinitsyn, Luyi Yang, Dwight G. Rickel, Dibyendu Roy, A. Greilich, M. Bayer, Scott A. Crooker

Published Oct 6, 2014• 50 citations
arXivHTMLPDF

Abstract

Per the fluctuation-dissipation theorem, the information obtained from spin fluctuation studies in thermal equilibrium is necessarily constrained by the system's linear response functions. However, by including weak radio frequency magnetic fields, we demonstrate that intrinsic and random spin fluctuations even in strictly unpolarized ensembles can reveal underlying patterns of correlation and coupling beyond linear response, and can be used to study nonequilibrium and even multiphoton coherent spin phenomena. We demonstrate this capability in a classical vapor of (41)K alkali atoms, where spin fluctuations alone directly reveal Rabi splittings, the formation of Mollow triplets and Autler-Townes doublets, ac Zeeman shifts, and even nonlinear multiphoton coherences.

DOI
10.1103/physrevlett.113.156601

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Per the fluctuation-dissipation theorem, the information obtained from spin fluctuation studies in thermal equilibrium is necessarily constrained by the system's linear response functions. However, by including weak radio frequency magnetic fields, we demonstrate that intrinsic and random spin fluctuations even in strictly unpolarized ensembles can reveal underlying patterns of correlation and coupling beyond linear response, and can be used to study nonequilibrium and even multiphoton coherent spin phenomena. We demonstrate this capability in a classical vapor of (41)K alkali atoms, where spin fluctuations alone directly reveal Rabi splittings, the formation of Mollow triplets and Autler-Townes doublets, ac Zeeman shifts, and even nonlinear multiphoton coherences.
Interacting multi-component spin systems are ubiquitous in nature and in the laboratory. As such, investigations of inter-species spin interactions are of vital importance. Traditionally, they are studied by experimental methods that are necessarily perturbative: e.g., by intentionally polarizing or depolarizing one spin species while detecting the response of the other(s). Here, we describe and demonstrate an alternative approach based on multi-probe spin noise spectroscopy, which can reveal inter-species spin interactions--under conditions of strict thermal equilibrium--by detecting and cross-correlating the stochastic fluctuation signals exhibited by each of the constituent spin species. Specifically, we consider a two-component spin ensemble that interacts via exchange coupling, and we determine cross-correlations between their intrinsic spin fluctuations. The model is experimentally confirmed using "two-color" optical spin noise spectroscopy on a mixture of interacting Rb and Cs vapors. Noise correlations directly reveal the presence of inter-species spin exchange, without ever perturbing the system away from thermal equilibrium. These non-invasive and noise-based techniques should be generally applicable to any heterogeneous spin system in which the fluctuations of the constituent components are detectable.
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 is emerging as a powerful technique for studying the dynamics of various spin systems also beyond their thermal equilibrium and linear response.In this context, we demonstrate a nonstandard mode of the spin-noise analysis applied to an out-of-equilibrium nonlinear atomic system realized by a Bell-Bloom atomic magnetometer.Driven by an external pump and undergoing a parametric excitation, this system is known to produce noise squeezing.Our measurements not only reveal a strong asymmetry in the noise distribution of the atomic signal quadratures at the magnetic resonance, but also provide insight into the mechanism behind its generation and evolution.In particular, a structure in the spectrum is identified which allows to investigate the main dependencies and the characteristic timescales of the noise process.The results obtained are compatible with parametrically induced noise squeezing.Notably, the noise spectrum provides information on the spin dynamics even in regimes where the macroscopic atomic coherence is lost, effectively enhancing the sensitivity of the measurements.Our Letter promotes spin-noise spectroscopy as a versatile technique for the study of noise squeezing in a wide range of spin-based magnetic sensors.
We analyze out-of-equilibrium fluctuations in a driven spin system and relate them to the noise of spin susceptibility. In the spirit of the linear response theory we further relate the noise of susceptibility to a 4-spin correlation function in equilibrium. We show that, in contrast to the second noise (noise of noise), the noise of susceptibility is a direct measure of non-Gaussian fluctuations in the system. We develop a general framework for calculating the noise of susceptibility using the Majorana representation of spin-1/2 operators. We illustrate our approach by a simple example of noninteracting spins coupled to a dissipative (Ohmic) bath.
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.
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.