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Advanced Quantum Technologies

Spin Polarization Measurement in SERF Comagnetometer Based on Phase‐Frequency Response of Magnetic Field

Ze Yu Cai, Feng Liu, Pengcheng Du, Kai Zhang, Linlin Yuan, Wenfeng Fan, Xusheng Lei, Wei Quan

Published Aug 1, 2024• 11 citations
Publisher

Abstract

Abstract This work presents an innovative approach for measuring the spin polarizations of coupled atomic ensembles in spin‐exchange relaxation‐free (SERF) comagnetometers, using the phase‐frequency response of the magnetic field. The zero‐phase point in the phase‐frequency response of the magnetic field along the ‐axis is examined to determine the deceleration factor and electronic magnetic field. Ultimately, the spin polarizations of electrons and noble‐gas atoms are calculated. The method is applied to test vapor cells with different parameters under various temperatures and pumping light intensities. The measurement errors caused by transverse electron relaxation of electronic spin polarization and nuclear spin polarization are 5.59% and 1.95% under high polarization, and 8.06% and 2.62% under low polarization. The measurement method features minimal impact on nuclear spin polarization and wide applicability compared to other methods, making it more applicable and suitable for SERF comagnetometers. This method has great significance in better understanding the system state of the SERF comagnetometer and improving its sensitivity.

DOI
10.1002/qute.202400127

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Abstract This work presents an innovative approach for measuring the spin polarizations of coupled atomic ensembles in spin‐exchange relaxation‐free (SERF) comagnetometers, using the phase‐frequency response of the magnetic field. The zero‐phase point in the phase‐frequency response of the magnetic field along the ‐axis is examined to determine the deceleration factor and electronic magnetic field. Ultimately, the spin polarizations of electrons and noble‐gas atoms are calculated. The method is applied to test vapor cells with different parameters under various temperatures and pumping light intensities. The measurement errors caused by transverse electron relaxation of electronic spin polarization and nuclear spin polarization are 5.59% and 1.95% under high polarization, and 8.06% and 2.62% under low polarization. The measurement method features minimal impact on nuclear spin polarization and wide applicability compared to other methods, making it more applicable and suitable for SERF comagnetometers. This method has great significance in better understanding the system state of the SERF comagnetometer and improving its sensitivity.
In this article, a highly sensitivein situmagnetic field fluctuation measurement method is proposed based on nuclear-spin depolarization in a spin-exchange relaxation-free (SERF) atomic comagnetometer (ACM). The steady-state model of the hybrid atomic spin ensemble is systematically studied. According to the theoretical model, two different states of nuclear-spin polarization and unpolarization lead to different sensitivities of the system to rotation and magnetic fields. The gradient magnetic field (GMF) is employed to change the state of nuclear-spin polarization of the noble gas, transforming the ACM into an atomic magnetometer (AM). The polarization and relaxation rates of the electron spin and nuclear spin under the two measurement modes are measured and compared by the magnetic resonance method and transient response method. At the same time, the performances in the ACM and AM are tested. Detailed experiments verify that the AM can achieve sensitivity for the magnetic field measurement with an average value of53.6 fT/Hz1/253.6~\mathbf {fT/Hz^{1/2}}53.6 fT/Hz1/2in the frequency range of10∼3010\sim 3010∼30Hz. The Allan variance method is adopted to evaluate thexxx- andyyy-axis magnetic field stabilities of the ACM, and the magnitudes are 61.6 and 55.9 fT at 100 s, contributing about 4.9×10−3  ∘/h\times 10\mathbf {^{-3}}\,\,\mathbf {^{\circ }/h}×10−3∘/hand 2.6×10−4  ∘/h\times 10\mathbf {^{-4}}\,\,\mathbf {^{\circ }/h}×10−4∘/hto the long-term stability of the ACM. This method can not only realize the high-sensitivityin situmeasurement of the close-to-zero magnetic field and its fluctuation but also realize the switching of the two measurement modes of rotation and magnetic field measurements, which is essential for the evaluation of magnetic field error.
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.
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.
Abstract Stochastic magnetic field noise has a non‐negligible negative impact on the performance of quantum precision measurement instruments such as spin‐exchange relaxation‐free (SERF) co‐magnetometer in terms of sensitivity and stability. Conventional magnetic field error analysis and suppression methods are not applicable to stochastic magnetic field noise. In this paper, a stochastic model of the SERF co‐magnetometer is proposed to analyze the mechanism of stochastic magnetic field noise. The mean and covariance propagation model of the SERF co‐magnetometer is given based on the stochasticity model and statistical principles. The analysis of simulation experiments reveals that reducing the longitudinal electron spin polarization can somewhat reduce the standard deviation of the system output caused by stochastic magnetic field noise. And the atomic ensembles are most resistant to stochastic magnetic field noise when the electron spin polarization strongly couples with the nuclear spin polarization. Finally, the experiments verified the above conclusions. In conclusion, this paper provides theoretical and experimental support for analyzing and suppressing the effect of stochastic magnetic field noise on the SERF co‐magnetometer, which is of great significance for improving the sensitivity and stability of the measurement.
The magnetic field response of a 87Rb-129Xe atomic spin comagnetometer operated in the spin-exchange relaxation-free (SERF) regime was investigated. The response model of the comagnetometer to the transverse magnetic fields along the y-axis and the x-axis considering the couple of electron spin and nuclear spin is presented. In the experiment, a high hybrid resonance peak near low-frequency was observed. By fitting the hybrid resonance with the presented response model, a pair of poles at 0.62 Hz and 1.8 Hz were obtained which correspond to the nuclear spin resonance and the electron spin resonance, respectively. The magnetic field response characteristic of the 87Rb-129Xe comagnetometer with different nuclear magnetic fields and electronic magnetic fields was simulated and analyzed. The simulation results indicate that the hybrid resonance frequency can be right-shifted by the larger nuclear magnetic field while the magnetic field suppression factor can be decreased by the larger electron magnetic field. This study is helpful to improve the performance of the atomic spin gyroscope based on the 87Rb-129Xe comagnetometer.
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.