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Physical Review A

Effects of spin-exchange collisions in a high-density alkali-metal vapor in low magnetic fields

Igor Savukov, Michael V. Romalis

Published Feb 10, 2005• 234 citations
Publisher

Abstract

Spin-exchange collisions often play a dominant role in the broadening of Zeeman resonances in an alkali-metal vapor. Contrary to intuitive expectations, at high alkali-metal densities this broadening can be completely eliminated by operating in a low magnetic field, allowing construction of ultrasensitive atomic magnetometers. We describe a detailed study of the Zeeman resonance frequencies and linewidths as a function of the magnetic field, alkali-metal density, and the degree of spin polarization of the atoms. Due to the nonlinear nature of the density matrix equations describing the spin-exchange collisions both the gyromagnetic ratio and the linewidth change as a function of the polarization. The results of experimental measurements are in excellent agreement with analytical and numerical solutions of the density matrix equations.

DOI
10.1103/physreva.71.023405

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Spin-exchange collisions often play a dominant role in the broadening of Zeeman resonances in an alkali-metal vapor. Contrary to intuitive expectations, at high alkali-metal densities this broadening can be completely eliminated by operating in a low magnetic field, allowing construction of ultrasensitive atomic magnetometers. We describe a detailed study of the Zeeman resonance frequencies and linewidths as a function of the magnetic field, alkali-metal density, and the degree of spin polarization of the atoms. Due to the nonlinear nature of the density matrix equations describing the spin-exchange collisions both the gyromagnetic ratio and the linewidth change as a function of the polarization. The results of experimental measurements are in excellent agreement with analytical and numerical solutions of the density matrix equations.
Spin-exchange collisions among alkali-metal atoms affect the coherence time and gyromagnetic ratio of atoms by redistributing the ground-state population. We theoretically study the interactions between magnetic fields and atoms in the presence of spin-exchange collisions. Using the modified Bloch equations derived from the density-matrix equation in a low spin-polarization limit, we obtain explicit formulas describing the role of spin-exchange collisions in the interactions between atoms and magnetic fields, especially the nonresonant radio-frequency fields, which are widely used to manipulate atoms. The results derived from these equations agree well with density-matrix simulations and previous experimental results, and provide a simple and precise way to quantitatively analyze the effect of spin-exchange collisions on atoms. Our paper is helpful to gain physical insight into the spin-exchange collisions and optimize the performance of atom-based precision measurement instruments.
We present an experimental and theoretical study of a scalar atomic magnetometer using an oscillating field-driven Zeeman resonance in a high-density optically pumped potassium vapor. We describe an experimental implementation of an atomic gradiometer with a noise level below $10\text{ }\text{fT}\text{ }{\text{Hz}}^{\ensuremath{-}1/2}$, fractional field sensitivity below ${10}^{\ensuremath{-}9}\text{ }{\text{Hz}}^{\ensuremath{-}1/2}$, and an active measurement volume of about 1.5 cm31.5\text{ }{\text{cm}}^{3}1.5 cm3. We show that the fundamental field sensitivity of a scalar magnetometer is determined by the rate of alkali-metal spin-exchange collisions even though the resonance linewidth can be made much smaller than the spin-exchange rate by pumping most atoms into a stretched spin state.
The study of magnetic-resonance linewidth is crucial in magnetic-resonance physics and its applications. Previous studies focused on the linewidth of alkali metal atoms within the spin-exchange relaxation-free regime near zero magnetic field and in strong magnetic fields where Zeeman resonances are well resolved due to the quadratic Zeeman effect. However, the linewidth in the unresolved-Zeeman-resonance regime, which is prevalent in various magnetometer and comagnetometer applications, is not well understood. To address this, we developed a theoretical framework based on the master equation for alkali metal atoms and solved it under the rotating-wave approximation and weak-driving conditions. Our numerical calculations and analytical expressions reveal that the light-narrowing effect occurs only when the ratio of the spin-exchange rate to the spin destruction rate exceeds a critical value. Additionally, we show that the linewidth in the unresolved Zeeman-resonance regime is significantly influenced by the mutual coupling of quantum coherence between different Zeeman sublevels. These findings provide a theoretical tool for understanding spin relaxation in alkali-metal atoms and optimizing the performance of atomic magnetometers and comagnetometers operating in this regime.
An effect is demonstrated where off-resonant optical pumping is enhanced by spin-exchange collisions, which enables a high degree of spin orientation to be obtained in alkali-metal atoms. The experiment with room-temperature cesium vapor employs radio-frequency spectroscopy under conditions of the nonlinear Zeeman effect that allow the populations of the individual Zeeman sublevels to be determined. The improved efficiency of atomic orientation leads to a significant reduction of population relaxation out of the state with maximum magnetic quantum number mmm (stretched state), which is observed as a narrowing of radio-frequency resonances. Spin-exchange collisions play a crucial role in this effect although the applied atomic density $\ensuremath{\sim}101010{}^{11}$ cm${}^{\ensuremath{-}3}$ corresponds to collision rates not greater than several tens of Hz. A simplified theoretical model has been developed to reproduce the measurement results numerically.
It was recently discovered that when there are sufficiently rapid spin-exchange collisions in an alkali-metal vapor, the rf magnetic-resonance frequency of the ground-state atoms becomes a constant fractional value (e.g., 411\frac{4}{11}114​ for Cs) of the Larmor frequency, and the linewidth becomes inversely proportional to the spin-exchange rate. These properties are in complete contrast to those in the slow spin-exchange limit. We present a theoretical analysis of these properties, and we predict some additional new effects for rapid spin exchange. Four theories are presented; an intuitive-vector model, a perturbation treatment, numerical solutions of complex non-Hermitian matrices, and a statistical analysis of the effect of rapid transfers between two Zeeman multiplets. These theories all provide, to varying degrees, consistent quantitative answers to the problem of how spin exchange affects magnetic resonance in an alkali vapor.
Abstract Spin-exchange (SE) and spin-destruction (SD) collisions play a central role in determining the coherence properties of alkali-metal vapors and the performance of alkali-metal magnetometers in external magnetic fields. In this work, we investigate how these collisions influence spin relaxation dynamics and magnetometric response using a generalized Bloch equation that fully accounts for the coupled evolution of spin polarizations in different hyperfine manifolds. Our results show that in the low-field regime, both SE and SD collisions contribute to the suppression of transverse spin relaxation and the slowdown of spin precession, whereas longitudinal relaxation depends weakly on the SE rate and is predominantly governed by SD interactions. Building on the established relationship between spin relaxation rates and magnetometric response, we further analyze how SE and SD collisions affect the performance of two representative magnetometer architectures: the spin-exchange relaxation-free (SERF) magnetometer and the magnetic-resonance Mx-type magnetometer. The SERF magnetometer’s response is found to be primarily determined by the SD rate, with only minor dependence on the nuclear spin quantum number. In contrast, the magnetic-resonance Mx-type magnetometer’s sensitivity is significantly affected by both the magnetic field strength and the SE rate. While the resonance linewidth decreases with reduced magnetic field, the associated measurement accuracy deteriorates markedly. Consequently, reliable magnetic field reconstruction is only achievable in the high-field regime, where the Larmor frequency greatly exceeds the SE rate.