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Chinese Physics B

Effects of spin-destruction and spin-exchange collisions on alkali-metal relaxation and magnetometric response

Feng Tang, Jianjun Li, Nan Zhao

Published Jan 14, 2026• 0 citations
Publisher

Abstract

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.

DOI
10.1088/1674-1056/ae37f7

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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.
Nuclear slowing-down factors account for the sharing of angular momentum between the electron and the nucleus in the effective Bloch description of alkali-metal spin dynamics in the spin-exchange-relaxation-free (SERF) regime. For collinear optical pumping and magnetic field, we find that longitudinal and transverse spin dynamics are characterized by different polarization-dependent slowing-down factors. Transverse dynamics are governed by the conventional factor q(p)q(p)q(p), with ppp the electron spin polarization, whereas longitudinal relaxation is governed by q(p)+p dq(p)/dpq(p)+p\,dq(p)/dpq(p)+pdq(p)/dp. The two factors coincide at zero polarization but differ substantially at high polarization, where the single-factor description overestimates the underlying pumping and relaxation rates inferred from longitudinal transients by factors approaching two to four, depending on the nuclear spin. We further derive closed-form expressions, valid at arbitrary polarization, for the residual spin-exchange relaxation of the transverse spin components at finite magnetic field along the pumping axis. This contribution is quadratic in the magnetic field and can become comparable to the zero-field linewidth at fields well within the SERF regime. The results are obtained by perturbation theory on the density-matrix dynamics linearized around the stationary state and are verified by numerical solutions of the microscopic density-matrix equation. These findings refine the effective Bloch description of alkali-metal spin dynamics and are directly relevant to atomic magnetometers and alkali-metal--noble-gas comagnetometers, including those used in precision searches for physics beyond the Standard Model.
High precision measurement of magnetic fields has been of great importance for both fundamental physics and practical applications. Magnetometers based on atomic spin effect provide a new technique for high precision measurement and have been enabled as the most sensitive magnetic sensors at present. However, the atomic spins used as probes to sense the magnetic fields are prone to the decoherence effects. For the atomic spin-exchange relaxation free (SERF) magnetometer which operates with high alkali atoms density in very low magnetic fields, the main relaxation mechanism is the spin-destruction collisions between atoms. In this paper, it is demonstrated by numerical simulations that the precision of the atomic SERF magnetometer is significantly affected by this spin-destruction collisions.
The spin-exchange relaxation-free (SERF) atomic magnetometer (AM) has vital importance in advanced research and has been widely applied in different fields. To improve the sensitivity and robustness of SERF magnetometers, understanding the relaxation mechanism is a significant approach. By controlling the amplitude and direction of external magnetic fields, and switching statuses of the pump and probe laser beam, we measured both the transverse and longitudinal relaxation rate in two experimental methods, respectively, and obtained the Larmor precession frequency, the spin-exchange relaxation rate, the spin-destruction relaxation rate, and the relaxation rate due to collisions between atoms and vapor cell walls. All experimental results are verified with the theoretical calculations. The final longitudinal relaxation rate of our magnetometer is 53 Hz. Furthermore, we measured the sensitivity of our SERF magnetometer reaching 5 fT/Hz1/2 from 5 to 70 Hz after differential measurement with the 3-dB bandwidth of 70 Hz. Our work helps to improve the detection capability of SERF magnetometers, providing performance assurance for searching for exotic spin-dependent interactions and applications, including magnetoencephalograms and magnetocardiograms.
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.
Abstract Nuclear magnetic resonance gyroscopes (NMRGs) employ noble-gas nuclear spins as inertial sensors and alkali-metal atoms as in-situ magnetometers. Heavy noble gases, particularly xenon, are widely used due to their long nuclear spin relaxation time and strong spin-exchange coupling with alkali-metal atoms. However, their presence introduces additional collisional mechanisms that affect the alkali-metal magnetic resonance linewidth, thereby influencing magnetometer sensitivity and overall gyro performance. In this work, we employ a theoretical framework based on the density matrix formalism and master equation approach to quantitatively study how xenon-induced two-body and three-body interactions modify the linewidth of alkali-metal atoms under realistic NMRG conditions. Our analysis reveals that Xe atoms primarily broaden the linewidth via binary spin-destruction collisions and van der Waals (vdW)-mediated F-damping processes, while the effect of Xe nuclear polarization is negligible at the ∼ 1 % level. We further demonstrate that nitrogen buffer gas plays a dual role: it directly contributes to alkali-metal spin relaxation through binary collisions and indirectly modulates vdW collision rates by altering molecular lifetimes. The interplay between these processes leads to an optimal nitrogen density that minimizes the linewidth. Additionally, we identify a temperature threshold above which light-narrowing emerges, with this threshold increasing alongside Xe density. These findings provide theoretical insight for optimizing spin relaxation control in alkali-metal magnetometers and improving NMRG performance.
Ultra sensitive detection and high precision measurement of magnetic fields have been of great importance for both fundamental physics and practical applications. Recent developments in the technology of atomic magnetometers have enabled the spin-exchange relaxation free (SERF) atomic magnetometers as the most sensitive devices for detecting and measuring static or quasi-static magnetic fields. In this paper, we analyze the effect of the most prominent relaxation mechanism (i.e., the spin-destruction collisions) on the precision of SERF magnetometers. For static magnetic fields, it is explicitly demonstrated how the spin-destruction collisions degrade the precision of the SERF magnetometers from the Heisenberg limit to the standard limit even with quantum resources being employed.