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Physical Review A

Suppression of spin-exchange relaxation in tilted magnetic fields within the geophysical range

Theo Scholtes, Szymon Pustelny, S. Fritzsche, V. Schultze, Ronny Stolz, Hans‐Georg Meyer

Published Jul 5, 2016• 26 citations
Publisher

Abstract

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 ${M}_{x}$ 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.

DOI
10.1103/physreva.94.013403

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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.
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.
Alkali-metal-vapor magnetometers, using coherent precession of polarized atomic spins for magnetic field measurement, have become one of the most sensitive magnetic field detectors. Their application areas range from practical uses such as detections of NMR signals to fundamental physics research such as searches for permanent electric dipole moments. One of the main noise sources of atomic magnetometers comes from the light shift that depends on the frequency of the pump laser. In this work, we theoretically study the light shift, taking into account the relaxation due to the optical pumping and the collision between alkali atoms and between alkali atoms and the buffer gas. Starting from a full master equation containing both the ground and excited states, we adiabatically eliminate the excited states and obtain an effective master equation in the ground-state subspace that shows an intuitive picture and dramatically accelerates the numerical simulation. Solving this effective master equation, we find that in the light-narrowing regime, where the line width is reduced while the coherent precession signal is enhanced, the frequency-dependence of the light shift is largely reduced, which agrees with experimental observations in cesium magnetometers. Since this effective master equation is general and is easily solved, it can be applied to an extensive parameter regime, and also to study other physical problems in alkali-metal-vapor magnetometers, such as heading errors.
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.
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.
Abstract We present a theoretical study of the optical-radio-frequency (rf) double resonance on hyperfine ground states of alkali-metal atoms in the geophysical magnetic-field range, in which resonance circularly polarized laser light is used in the optical pumping and detection processes. The analytical expressions of the rf resonance signals corresponding to two ground states are obtained based on atomic multipole moments, where the alignment effect is considered and that is responsible for the resonance shape and linewidth especially when the optical power is relatively strong. In addition, we also obtain the analytical expressions of the linewidths of two separated resonance peaks and one presenting the competition process of the optical pumping, rf field and spin-exchange collision. Two different types of light narrowing phenomena are investigated by comparing the longitudinal relaxation rates of atomic multipole moments for two ground states. Applied to rubidium and cesium atoms, we show a particularly close agreement of our analytical results with more elaborate calculations using density-matrix theory. Our theoretical model is relevant for optimizing the sensitivity of magnetometers.
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.