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IEEE Transactions on Instrumentation and Measurement

Measurement of Equilibrium Spin Polarization in Spin-Exchange Relaxation-Free Atomic Magnetometers via the Steady-State Response to the Triaxial Magnetic Field

Faming Wang, Xiujie Fang, Bozheng Xing, Yueshen Wang, Jianli Li, Jiaming Liu, Yueyang Zhai, Danyue Ma

Published Jan 1, 2025• 7 citations
Publisher

Abstract

This study proposes an in situ method for measuring the equilibrium spin polarization and its longitudinal spatial distribution in a spin-exchange relaxation-free (SERF) atomic magnetometer. The total relaxation rate was determined by analyzing the steady-state response of the magnetometer to the triaxial magnetic field. The transfer coefficient between spin polarization along the probe beam axis and the steady-state response was derived from the optical depth of the probe light and the incident/transmitted power through the vapor cell. By applying a DC magnetic field along the sensitive axis and combining the total relaxation rate with the transfer coefficient, the equilibrium spin polarization value under zero-field conditions was obtained. The equilibrium spin polarization distribution along the pump beam propagation direction was measured, showing consistent trends with simulation results, with a maximum relative error of less than 5%. The expanded uncertainty of the proposed equilibrium spin polarization measurement method ranges from 0.8% to 9.7%. The advantages of this method include no requirement for additional optical field or magnetic field modulation, immunity to temperature and temperature gradients, and the capability to directly determine the equilibrium spin polarization value.

DOI
10.1109/tim.2025.3619263

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This study proposes an in situ method for measuring the equilibrium spin polarization and its longitudinal spatial distribution in a spin-exchange relaxation-free (SERF) atomic magnetometer. The total relaxation rate was determined by analyzing the steady-state response of the magnetometer to the triaxial magnetic field. The transfer coefficient between spin polarization along the probe beam axis and the steady-state response was derived from the optical depth of the probe light and the incident/transmitted power through the vapor cell. By applying a DC magnetic field along the sensitive axis and combining the total relaxation rate with the transfer coefficient, the equilibrium spin polarization value under zero-field conditions was obtained. The equilibrium spin polarization distribution along the pump beam propagation direction was measured, showing consistent trends with simulation results, with a maximum relative error of less than 5%. The expanded uncertainty of the proposed equilibrium spin polarization measurement method ranges from 0.8% to 9.7%. The advantages of this method include no requirement for additional optical field or magnetic field modulation, immunity to temperature and temperature gradients, and the capability to directly determine the equilibrium spin polarization value.
A novel method to determine the spin polarization and its distribution for a spin-exchange relaxation-free (SERF) atomic magnetometer are proposed in this paper. The Larmor precession frequency is measured using the fast Fourier transform (FFT) analysis result of the transient response of the magnetometer under the excitation of a series of the step-changed magnetic field. The spin polarization is extracted from the slow-down factor of the precession frequency. The variation of the spin polarization with different pump light intensities and the distribution of the spin polarization along the direction of the pump light are analyzed, and the experimental results are well consistent with the theoretical predictions. The expanded uncertainties of the experimental results vary from 2% to 11% with the increase of the spin polarization and the reason for this variation is analyzed. The advantage of this method is that it allows the accurate measurement of the spin polarization in the pump beam direction within the SERF regime operating state, and it is unaffected by the large optical depth of the vapor cell.
The electronic spin polarization of alkali-metal-vapor atoms is a pivotal parameter for atomic magnetometers. Herein, a novel method is presented for determining the spin polarization with a miniaturized single-beam spin-exchange-relaxation-free (SERF) magnetometer on the basis of zero-field cross-over resonance. Two separate laser beams are utilized to heat the cell and interrogate the vapor atoms, respectively. Spin polarization can be extracted by measuring the resonance response signal of the magnetometer to the transverse magnetic field under different irradiances. Results of these experiments are consistent well with the theoretical predictions with the maximum deviation less than 4%. The proposed method has the integrated advantages of possessing a simple configuration and in-situ measurement. Furthermore, combined with a homemade optical differential detection system with a factor of approximately three of the power noise suppression, the developed single-beam SERF atomic magnetometer with a measuring sensitivity of 32 fT/Hz 1/2 has been achieved. This demonstrated approach can help guide the development of chip-scale atomic magnetometers for bio-magnetic field imaging applications.
The measurement of atomic spin polarization distribution in spin-exchange relaxation free (SERF) magnetometer is an important topic for improving the sensitivity and consistency of multi-channel magnetic field measurement applications. A novel spin polarization spatial distribution measurement method is presented based on the transient response of the magnetometer after modulating the pumped light with a chopper. Polarization is obtained by a slow-down factor based on the fast spin-exchange interaction effects. Longitudinal and transverse polarization distributions are measured simultaneously without interrupting the operation of the SERF status. Under different oscillating magnetic fields, the spin polarization is measured at the cell centroid. Residual magnetic field inside the magnetometer is obtained from the linear relationship between the precession frequency and the oscillating magnetic field. The one-dimensional polarization distributions in the x, y, and z axes are measured using a digital micromirror device with a resolution of 0.25 cm. The measurement results conform to the Lambert-Bier absorption law and the Gaussian distribution law. Furthermore, 7 × 7 two-dimensional spatial distribution measurements of polarization on the xy and yz planes are performed. Nonuniformity of 1.04 in the xy plane and 1.82 in the yz plane in the built magnetometer. Compared with other measurement methods, the distribution measurement method proposed is independent of optical depth and suitable for low polarization and high polarization applications. Based on the results of the proposed measurement method of spin polarization spatial distribution, further compensation can improve the application consistency of multi-channel magnetic field measurements and improve the sensitivity of single-channel differential measurements.
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.
The spin-exchange-relaxation-free (SERF) atomic magnetometer is an ultra-high sensitivity magnetometer, but it must be operated in a magnetic field with strength less than about 10 nT. Magnetic field compensation is an effective way to shield the magnetic field, and this paper demonstrates an in situ triaxial magnetic field compensation system for operating the SERF atomic magnetometer. The proposed hardware is based on optical pumping, which uses some part of the SERF atomic magnetometer itself, and the compensation method is implemented by analyzing the dynamics of the atomic spin. The experimental setup for this compensation system is described, and with this configuration, a residual magnetic field of strength less than 2 nT (±0.38 nT in the x axis, ±0.43 nT in the y axis, and ±1.62 nT in the z axis) has been achieved after compensation. The SERF atomic magnetometer was then used to verify that the residual triaxial magnetic fields were coincident with what were achieved by the compensation system.
A method of measuring in-situ magnetic field gradient is proposed in this paper. The magnetic shield is widely used in the atomic magnetometer. However, there is magnetic field gradient in the magnetic shield, which would lead to additional gradient broadening. It is impossible to use an ex-situ magnetometer to measure magnetic field gradient in the region of a cell, whose length of side is several centimeters. The method demonstrated in this paper can realize the in-situ measurement of the magnetic field gradient inside the cell, which is significant for the spin relaxation study. The magnetic field gradients along the longitudinal axis of the magnetic shield are measured by a spin-exchange relaxation-free (SERF) magnetometer by adding a magnetic field modulation in the probe beam’s direction. The transmissivity of the cell for the probe beam is always inhomogeneous along the pump beam direction, and the method proposed in this paper is independent of the intensity of the probe beam, which means that the method is independent of the cell’s transmissivity. This feature makes the method more practical experimentally. Moreover, the AC-Stark shift can seriously degrade and affect the precision of the magnetic field gradient measurement. The AC-Stark shift is suppressed by locking the pump beam to the resonance of potassium’s D1 line. Furthermore, the residual magnetic fields are measured with σ + - and σ – -polarized pump beams, which can further suppress the effect of the AC-Stark shift. The method of measuring in-situ magnetic field gradient has achieved a magnetic field gradient precision of better than 30 pT/mm.