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Physical Review Letters

High-Sensitivity Atomic Magnetometer Unaffected by Spin-Exchange Relaxation

J. C. Allred, ROBERT LYMAN, Thomas W. Kornack, Michael V. Romalis

Published Sep 9, 2002• 1,050 citations
Publisher

Abstract

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 $2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}18}\text{ }\mathrm{T}\text{ }\mathrm{H}{\mathrm{z}}^{\mathrm{\ensuremath{-}}\mathrm{1}\mathrm{/}\mathrm{2}}$.

DOI
10.1103/physrevlett.89.130801

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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 fT Hz\ensuremath−1/210\text{ }\mathrm{f}\mathrm{T}\text{ }\mathrm{H}{\mathrm{z}}^{\mathrm{\ensuremath{-}}\mathrm{1}\mathrm{/}\mathrm{2}}10 fT Hz\ensuremath−1/2, 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×\else\texttimes\fi10\ensuremath−18 T Hz\ensuremath−1/22\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}18}\text{ }\mathrm{T}\text{ }\mathrm{H}{\mathrm{z}}^{\mathrm{\ensuremath{-}}\mathrm{1}\mathrm{/}\mathrm{2}}2\ifmmode×\else\texttimes\fi10\ensuremath−18 T Hz\ensuremath−1/2.
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.
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.
Present protocols for obtaining the ultimate magnetic sensitivity of optically pumped magnetometers (OPMs) utilizing alkali-metal ensembles rely on uncorrelated atoms in stretched states. A new approach for calculating the spin projection noise (SPN)-limited signal to noise ratio (SNR) and the magnetic sensitivity of OPMs is proposed. Our model is based solely on the mean-field density matrix dynamics and in contrast to previous models, it applies to both low and high field regimes, it takes into account the degree of spin polarization, the intra- and interhyperfine correlations, the decoherence processes, the atom-light coupling and the effects of the spin dynamics on the spin-noise spectra. Fine tuning of the probe frequency allow us to explore different hyperfine states and ground-state correlations. Especially in the spin-exchange-relaxation-free (SERF) regime, alongside the magnetic resonance narrowing and the increased number density, hallmarks of SERF magnetometers, we report on a new SERF feature; the reduction of spin-projection noise at the spin precession frequency as a consequence of strongly-correlated hyperfine spins that attenuate and redistribute SPN when properly probed.
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.
Spin noise sets fundamental limits to the precision of measurements using spin-polarized atomic vapors, such as performed with sensitive atomic magnetometers. Spin squeezing offers the possibility to extend the measurement precision beyond the standard quantum limit of uncorrelated atoms. Contrary to current understanding, we show that, even in the presence of spin relaxation, spin squeezing can lead to a significant reduction of spin noise, and hence an increase in magnetometric sensitivity, for a long measurement time. This is the case when correlated spin relaxation due to binary alkali-atom collisions dominates independently acting decoherence processes, a situation realized in thermal high atom-density magnetometers and clocks.
We describe a Cs atomic magnetometer operating in the spin-exchange-relaxation-free (SERF) regime. With a vapor cell temperature of $103\text{ }\ifmmode^\circ\else\textdegree\fi{}\text{C}$ we achieve intrinsic magnetic resonance widths $\ensuremath{\Delta}B=17\text{ }\ensuremath{\mu}\text{G}$ corresponding to an electron spin-relaxation rate of $300\text{ }{\text{s}}^{\ensuremath{-}1}$ when the spin-exchange rate is ${\ensuremath{\Gamma}}_{\text{SE}}=14\text{ }000\text{ }{\text{s}}^{\ensuremath{-}1}$. We also observe an interesting narrowing effect due to diffusion. Signal-to-noise measurements yield a sensitivity of about 400 pG/Hz400\text{ }\text{pG}/\sqrt{\text{Hz}}400 pG/Hz​. Based on photon shot noise, we project a sensitivity of 40 pG/Hz40\text{ }\text{pG}/\sqrt{\text{Hz}}40 pG/Hz​. A theoretical optimization of the magnetometer indicates sensitivities on the order of 2 pG/Hz2\text{ }\text{pG}/\sqrt{\text{Hz}}2 pG/Hz​ should be achievable in a 1 cm31\text{ }{\text{cm}}^{3}1 cm3 volume. Because Cs has a higher saturated vapor pressure than other alkali metals, SERF magnetometers using Cs atoms are particularly attractive in applications requiring lower temperatures.