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Physical Review A

Measurement of transverse spin-relaxation rates in a rubidium vapor by use of spin-noise spectroscopy

George E. Katsoprinakis, Argyrios T. Dellis, Iannis K. Kominis

Published Apr 12, 2007• 59 citations
Publisher

Abstract

Spin noise sets fundamental limits to the attainable precision of measurements using spin-polarized atomic vapors and therefore merits a careful study. On the other hand, it has been recently shown that spin noise contains useful physical information about the atomic system, otherwise accessible via magnetic-resonance-type experiments. We here show in yet another manifestation of the fluctuation-dissipation theorem, that spin noise reveals information on the spin-coherence dissipation properties of the atomic system, described by $1∕{T}_{2}$, the transverse spin-relaxation rate. We present the high-resolution measurements of spin noise at a low magnetic field, leading to an accurate comparison of the extracted relaxation rates with the ones inferred from traditional magnetic-resonance-type measurements in optical pumping experiments.

DOI
10.1103/physreva.75.042502

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Spin noise sets fundamental limits to the attainable precision of measurements using spin-polarized atomic vapors and therefore merits a careful study. On the other hand, it has been recently shown that spin noise contains useful physical information about the atomic system, otherwise accessible via magnetic-resonance-type experiments. We here show in yet another manifestation of the fluctuation-dissipation theorem, that spin noise reveals information on the spin-coherence dissipation properties of the atomic system, described by 1∕T21∕{T}_{2}1∕T2​, the transverse spin-relaxation rate. We present the high-resolution measurements of spin noise at a low magnetic field, leading to an accurate comparison of the extracted relaxation rates with the ones inferred from traditional magnetic-resonance-type measurements in optical pumping experiments.
The spin transverse relaxation time ( T 2 ) of atoms is an important indicator for magnetic field precision measurement. Especially in optically-pumped atomic magnetometer, the linewidth of the magnetic resonance signal is one of the most important parameters of sensitivity, which is inversely correlated with T 2 of atoms. In this paper, we propose four methods, namely spin noise spectroscopy signal fitting, radio-frequency free induction decay (RF-FID) signal fitting, ω m (modulation frequency)-broadening fitting, and magnetic resonance broadening fitting, for in-situ measurement T 2 of atomic vapor cells based on light-atom interactions. Meanwhile, T 2 of three Rubidium (Rb) atomic vapor cells with different parameters are measured and discussed by using these four methods. A comparative analysis visualizes the characteristics of the different methods and the effects of buffer gas on T 2 of Rb atoms. Through theoretical and experimental analysis, we assess the applicability of each method and concluded that the RF-FID signal fitting method provides the most accurate measurements due to the timing sequence control system, which results in a cleaner measurement environment. Furthermore, we demonstrate and qualitatively analyze the relationship between temperature and T 2 of Rb atoms. This work may offer valuable insights into the selection of atomic vapor cells and it is also applicable for the spin-exchange relaxation-free region.
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.
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.
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.
We report noninvasive detection of spin coherence in a collection of Raman-driven cold atoms using dispersive Faraday rotation fluctuation measurements, which opens possibilities of probing spin correlations in quantum gases and other similar systems. We demonstrate five orders of magnitude enhancement of the measured signal strength as compared to traditional spin noise spectroscopy with thermal atoms in equilibrium. Our observations are in good agreement with the comprehensive theoretical modeling of the driven atoms at various temperatures. The extracted spin relaxation rate of cold rubidium atoms with atom number density $\ensuremath{\sim}10{\phantom{\rule{0.16em}{0ex}}}^{9}/{\mathrm{cm}}^{3}$ is of the order of $3\phantom{\rule{0.16em}{0ex}}\ifmmode\times\else\texttimes\fi{}\phantom{\rule{0.16em}{0ex}}10{\phantom{\rule{0.16em}{0ex}}}^{3}\phantom{\rule{4pt}{0ex}}{\mathrm{s}}^{\ensuremath{-}1}$ at 150 $\ensuremath{\mu}\mathrm{K}$, two orders of magnitude less than $3\phantom{\rule{0.16em}{0ex}}\ifmmode\times\else\texttimes\fi{}\phantom{\rule{0.16em}{0ex}}10{\phantom{\rule{0.16em}{0ex}}}^{5}\phantom{\rule{4pt}{0ex}}{\mathrm{s}}^{\ensuremath{-}1}$ of that of a thermal atomic vapor with atom number density $\ensuremath{\sim}10{\phantom{\rule{0.16em}{0ex}}}^{12}/{\mathrm{cm}}^{3}$ at 373 K.
Traditional practice of suppressing low-frequency noise in atomic magnetometers is mainly through the application of magnetic field modulation, while magnetic fields of this kind introduce extra transverse relaxation, which results in a decrease of sensitivity. In this study, a novel method of measuring relaxation rate induced by spin-destruction, wall collisions and modulation magnetic fields is proposed. The optical pumping model is studied both in optical-thin and optical-thick vapor cell through the analysis of total relaxation, thus the optical pumping rate can be separated from total relaxation by analyzing the optical depth. Furthermore, based on the analysis of optical pumping rate and relaxation rate, the polarization of the electron ensemble was evaluated. A compact magnetometer with single-beam configuration is developed for the proof of concept, and the experimental results show good agreements with theoretical calculation. Our method provides a simple and feasible approach to in-situ measurement of transverse relaxation rate and optical pumping rate with physical structure of the device untouched, which is especially advantageous for designing and optimizing compact atomic magnetometers.