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Advanced Quantum Technologies

Measurement of Relaxation Rates for NMOR Atomic Magnetometers Based on the Transient Dynamics

Zhenglong Lu, Jiali Liu, Xin Zhao, Yanchao Chai, Changhao Zhang, Junlin Chen, Jie Yang, Liwei Jiang

Published Jan 1, 2026• 0 citations
Publisher

Abstract

Abstract The relaxation rate is a fundamental parameter that characterizes the dynamics of atomic ensembles and plays a critical role in the performance of atomic magnetometers. In this study, a transient dynamics model for the NMOR magnetometer is developed based on multipole moment theory, revealing that the decay rate of the transient response to a step magnetic field from zero to certain value is determined by both transverse and longitudinal relaxation rates, whereas that to a step magnetic field from certain value to zero depends solely on the longitudinal relaxation rate. This distinction enables the independent determination of the two relaxation rates. To validate the proposed method, transverse and longitudinal relaxation rates are experimentally measured under various laser powers, which are consistent with the Lorentzian linewidths extracted from magnetic resonance curve fitting. This study provides valuable insights into atomic transient dynamics and contributes to the fast measurement of relaxation rates in NMOR magnetometers.

DOI
10.1002/qute.202500442

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Abstract The relaxation rate is a fundamental parameter that characterizes the dynamics of atomic ensembles and plays a critical role in the performance of atomic magnetometers. In this study, a transient dynamics model for the NMOR magnetometer is developed based on multipole moment theory, revealing that the decay rate of the transient response to a step magnetic field from zero to certain value is determined by both transverse and longitudinal relaxation rates, whereas that to a step magnetic field from certain value to zero depends solely on the longitudinal relaxation rate. This distinction enables the independent determination of the two relaxation rates. To validate the proposed method, transverse and longitudinal relaxation rates are experimentally measured under various laser powers, which are consistent with the Lorentzian linewidths extracted from magnetic resonance curve fitting. This study provides valuable insights into atomic transient dynamics and contributes to the fast measurement of relaxation rates in NMOR magnetometers.
The sensitivity and bandwidth (BW) as the primary criteria of spin-exchange relaxation-free (SERF) atomic magnetometer (AM) are closely related to the transverse relaxation rate of atomic ensemble. In this study, we show an effective method for transverse relaxation rate measurement drawing on the golden Section algorithm. With no requirement of offline fitting, the measuring time of this method is only 7 s. This is especially advantageous for reducing measurement errors due to the drifts of spatial magnetic field and light intensity and using multiple measurements to better monitor the performance of magnetometers. Moreover, the reset after measuring is optimized as the sensitive axis magnetic field correction, ensuring the integrity of measurement while improving the accuracy of magnetic compensation. Furthermore, we find that the acquired experimental data using this method can be adopted for the evaluation of magnetic field compensation performance and the monitoring of magnetic anomaly states. This determination method for transverse relaxation rate is anticipated to play a greater important role in multichannel SERF AMs’ arrays.
The magnitude of the electron spin-relaxation rate Rrel of the atomic ensemble directly affects the sensitivity of the spin-exchange relaxation-free (SERF) atomic magnetometer (AM). The rapid and in-situ characterization of Rrel is of great importance. In this work, a fast extraction method of Rrel is proposed with a measurement period shorten to 0.5 s, merely detecting the transient response of SERF AM to a transverse DC excitation magnetic field after switching off the pump beam. In contrast to the conventional methods based on the measurement of the magnetic resonance linewidth, this method circumvents the involvement of optical pumping rate, and enables monitoring Rrel under arbitrary polarization, which is expected to improve the authenticity of Rrel measurement in a more convenient way.
The spin-exchange relaxation of electron spins directly affects the sensitivity of the atomic magnetometers. Rapid determination of the spin-exchange relaxation is essential. In this work, we propose a novel method for measuring the spin-exchange relaxation that allows being operated in the range of zero to earth-scale magnetic field. The longitudinal and transverse relaxation are synchronously extracted from the magnetic resonance linewidth and radio-frequency field amplitude corresponding to the maximum slope of the dispersive resonance curve. The spin-exchange relaxation is further obtained from the difference. The experimental results are consistent with the conventional linewidth fitting method in near-zero magnetic field and with the theoretical expectation in earth-scale magnetic field. This method not only improves authenticity compared to the conventional linewidth fitting method by considering the effect of rf field on relaxation, but also provides a fast and reliable measurement of the spin-exchange relaxation in earth-scale field.
The transverse relaxation time (T2) is an important indicator to determine the fundamental sensitivity limit of alkali-metal atomic magnetometers. We propose a method based on the principle of longitudinal field modulation that obtains T2 by scanning the transverse static magnetic field. The previous technique of extracting T2 from the linewidth of the modulation frequency and the traditional magnetic-resonance-broadening-fitting method are also described. The T2 measurements of Cesium (Cs) atoms are carried out through these three methods, whose operating environments are applicable to different atomic magnetometers, respectively. The method that we propose can be used for obtaining the T2 of Cs atoms as well as detecting the transverse static magnetic field and is customized for the study of the Cs–Xenon ensemble for the construction of nuclear magnetic resonance gyroscopes. Moreover, the relationship between the limit sensitivities and cell temperatures is further studied in the experiment.
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.
Maintaining a near-zero magnetic field condition is a requisite for atomic magnetometer under the spin-exchange relaxation-free (SERF) regime. Therefore, the precise determination of the residual magnetic fields is of great significance. Herein, we proposed an in-situ measurement method of residual magnetic fields in a dual-beam atomic magnetometer based on a transient response of the transverse polarization along the probe beam direction after switching off the pump beam. Proceeding from the Bloch equation, we established a complete evolution expression of the polarization vector under any static residual magnetic field with the pump beam switched off. On this basis, we analyzed the transient response of the transverse polarization by numerical simulation under different situations of residual magnetic fields. Besides, we also considered two possible conditions when the residual magnetic fields are relatively large or small, respectively. Accordingly, we presented an efficient and convenient estimation method of the residual magnetic fields based on certain time characteristics of the transient response. We verified the feasibility of our method by experiment and achieved a triaxial residual magnetic fields measurement within 0.5 s. This method can realize an in situ and real-time measurement of the residual magnetic fields in a fast and convenient way. Furthermore, this method can evaluate the effectiveness of different magnetic field compensation methods without introducing any modulation or extra devices.