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Physical Review A

Spin-exchange narrowing of the atomic ground-state resonances

Witold Chałupczak, Patrick Josephs-Franks, Brian Patton, Szymon Pustelny

Published Oct 21, 2014• 19 citations
Publisher

Abstract

At the most fundamental level, the performance of atomic sensors is limited by quantum decoherence. The problem of decoherence has been addressed at low magnetic fields with atomic samples, where the limiting factor of the coherence lifetime arises from spin-exchange collisions. In this paper, we demonstrate the complex role of the collisions in the relaxation of quantum states of alkali-metal atoms. The detailed understanding of the collision role allows us to reduce the ground-state relaxation in stronger magnetic fields (tens $\ensuremath{\mu}\mathrm{T}$). Reduction of the relaxation rate enables improvement of the performance of atomic sensors. In particular, enhancement of the sensitivity of optical magnetometers in the detection of stronger magnetic fields may be obtained. Reduced transverse relaxation also enables increasing quantum-information storage time in atomic vapor.

DOI
10.1103/physreva.90.042509

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Physical Review Letters•Sep 9, 2002•1,050 citations
At the most fundamental level, the performance of atomic sensors is limited by quantum decoherence. The problem of decoherence has been addressed at low magnetic fields with atomic samples, where the limiting factor of the coherence lifetime arises from spin-exchange collisions. In this paper, we demonstrate the complex role of the collisions in the relaxation of quantum states of alkali-metal atoms. The detailed understanding of the collision role allows us to reduce the ground-state relaxation in stronger magnetic fields (tens \ensuremathμT\ensuremath{\mu}\mathrm{T}\ensuremathμT). Reduction of the relaxation rate enables improvement of the performance of atomic sensors. In particular, enhancement of the sensitivity of optical magnetometers in the detection of stronger magnetic fields may be obtained. Reduced transverse relaxation also enables increasing quantum-information storage time in atomic vapor.
Spin-exchange relaxation-free magnetometers based on dense ensembles of alkali-metal spins are precision quantum sensors that hold the record of measured and projected sensitivity to magnetic fields, in the microgauss to milligauss range. At geomagnetic fields however, these sensors quickly lose their magnetic sensitivity due to spin decoherence by random spin-exchange collisions. Here we discover that atoms with nuclear spin I=12I=\frac{1}{2}I=21​ can operate in the spin-exchange relaxation-free regime even at high magnetic field. We counterintuitively show that frequent collisions between a dense and optically inaccessible (I=12)(I=\frac{1}{2})(I=21​) gas with another optically accessible spin gas (I>12I>\frac{1}{2}I>21​) improve the fundamental magnetic sensitivity of the latter. We analyze the performance of a dual-species potassium and atomic hydrogen magnetometer and project a fundamental sensitivity of about 10aT(cm3/Hz)1/210\phantom{\rule{0.28em}{0ex}}\mathrm{aT}\phantom{\rule{0.16em}{0ex}}{({\mathrm{cm}}^{3}\text{/}\mathrm{Hz})}^{1/2}10aT(cm3/Hz)1/2 at geomagnetic fields for feasible experimental conditions.
We present a detailed experimental and theoretical study on the relaxation of spin coherence due to the spin-exchange mechanism arising in the electronic ground states of alkali-metal vapor atoms. As opposed to the well-explored formation of a stretched state in a longitudinal geometry (magnetic field parallel to the laser propagation direction) we employ adapted hyperfine-selective optical pumping in order to suppress spin-exchange relaxation. By comparing measurements of the intrinsic relaxation rate of the spin coherence in the ground state of cesium atoms with detailed density-matrix simulations we show that the relaxation due to spin-exchange collisions can be reduced substantially even in a tilted magnetic field of geomagnetic strength, the major application case of scalar magnetic surveying. This explains the observed striking improvement in sensitivity and further deepens the understanding of the light-narrowed Mx{M}_{x}Mx​ magnetometer, which was presented recently. Additionally, new avenues for investigating the dynamics in alkali-metal atoms governed by the spin-exchange interaction and interacting with arbitrary external fields open up.
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.
In this paper, a new type of high-sensitivity magnetometer that can surpass SQUID magnetometers operating in liquid-helium in sensitivity and spatial resolution is discussed. The sensitivity of atomic magnetometers is determined by the electron spin relaxation time and the number of alkali-metal atoms. The relaxation time is usually limited by spin-exchange collisions between atoms and drops at higher alkali-metal density. Spin-exchange collisions preserve the total spin of the atoms, but can change their hyperfine state, which reverses the direction of spin precession in the magnetic field. Thus, spin-exchange collisions usually cause spin decoherence. However, this relaxation process can be suppressed if the spin precession frequency is much smaller than the rate of spin-exchange collisions. These conditions lead to 'motional narrowing', where the spin precession angle between the collisions is so small that the atoms do not lose coherence. A magnetometer operating near zero magnetic field can simultaneously achieve high alkali-metal density and long spin-relaxation time, resulting in very high sensitivity.
For spin-polarized ensembles of alkali-metal atoms with hyperfine structure and spin greater than 1/2, the interplay between spin dynamics and quantum noise mechanisms remains largely unexplored, especially in the spin-exchange-relaxation-free (SERF) regime. In particular, the theoretical understanding of the dynamics for the mean values of the spin operators was established shortly after the advent of optical pumping. In contrast, a corresponding theory for spin fluctuations has not yet been developed, and is addressed in this work. Here, we develop such a first-principles theory of spin fluctuations in alkalimetal vapors. The nonlinearity bottleneck of spin-exchange collisions, which dominate the physics of such vapors, is overcome by linearizing the dynamics around the equilibrium density matrix. The result is a precise calculation of the absolute magnetic sensing limit of optically pumped atomic magnetometers, which can precisely benchmark quantum limited and quantum enhanced protocols, in contrast to the traditional approach shown to be adequate only within a factor of 2. Further, we elucidate how signal and noise in atomic magnetometers are distributed among the spin eigenmodes defined under continuous optical pumping and probing via the paramagnetic Faraday rotation. Notably, in the SERF regime, alongside the magnetic resonance narrowing, we find a reduction of spin noise at the spin-precession frequency as a consequence of strong hyperfine correlations redistributing spin noise, when both hyperfine manifolds are simultaneously probed. These insights can lead to improved quantum devices utilizing alkali-metal atoms or similar spin-based sensing platforms.
Alkali-metal magnetometers compete with SQUID detectors as the most sensitive magnetic field sensors. Their sensitivity is limited by relaxation due to spin-exchange collisions. We demonstrate a K magnetometer in which spin-exchange relaxation is completely eliminated by operating at high K density and low magnetic field. Direct measurements of the signal-to-noise ratio give a magnetometer sensitivity of $10\text{ }\mathrm{f}\mathrm{T}\text{ }\mathrm{H}{\mathrm{z}}^{\mathrm{\ensuremath{-}}\mathrm{1}\mathrm{/}\mathrm{2}}$, limited by magnetic noise produced by Johnson currents in the magnetic shields. We extend a previous theoretical analysis of spin exchange in low magnetic fields to arbitrary spin polarizations and estimate the shot-noise limit of the magnetometer to be $2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}18}\text{ }\mathrm{T}\text{ }\mathrm{H}{\mathrm{z}}^{\mathrm{\ensuremath{-}}\mathrm{1}\mathrm{/}\mathrm{2}}$.