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Advanced Quantum Technologies

Zero‐Position Closed‐Loop Control of Nuclear Spin in a K‐Rb‐21Ne$^{21}{\rm Ne}$ Comagnetometer

Longyan Ma, Hongyu Pei, Lihong Duan, Xiaohan Ge, Wenfeng Fan, Wei Quan

Published Mar 17, 2025• 4 citations
Publisher

Abstract

Abstract In SERF (spin‐exchange relaxation‐free) comagnetometers, the fluctuation of the atomic ensemble's polarization significantly impacts the long‐term stability of the output signal. A real‐time closed‐loop control method for the nuclear spin polarization is proposed, and the measurement model is established using Kalman state observer. Furthermore, magnetic field control signals are generated using a proportional‐integral‐derivative (PID) strategy, which is then applied to the atomic ensemble to dynamically adjust the nuclear spin polarization. Finally, closed‐loop control of nuclear spin polarization is achieved through continuous feedback and control. Moreover, experiments have demonstrated that implementing a closed‐loop system for nuclear spin zero‐position is conducive to reducing the sensitivity of the output signal to fluctuations in the external environment. The experimental results show that the Allan deviation at 100 s is reduced by , and the sensitivity of inertial rotation measurement is significantly improved, that is, the noise level at 1 Hz is suppressed by approximately .

DOI
10.1002/qute.202400432

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Zero‐Position Closed‐Loop Control of Nuclear Spin in a K‐Rb‐21Ne21Ne^{21}{\rm Ne}21Ne Comagnetometer
Abstract In SERF (spin‐exchange relaxation‐free) comagnetometers, the fluctuation of the atomic ensemble's polarization significantly impacts the long‐term stability of the output signal. A real‐time closed‐loop control method for the nuclear spin polarization is proposed, and the measurement model is established using Kalman state observer. Furthermore, magnetic field control signals are generated using a proportional‐integral‐derivative (PID) strategy, which is then applied to the atomic ensemble to dynamically adjust the nuclear spin polarization. Finally, closed‐loop control of nuclear spin polarization is achieved through continuous feedback and control. Moreover, experiments have demonstrated that implementing a closed‐loop system for nuclear spin zero‐position is conducive to reducing the sensitivity of the output signal to fluctuations in the external environment. The experimental results show that the Allan deviation at 100 s is reduced by , and the sensitivity of inertial rotation measurement is significantly improved, that is, the noise level at 1 Hz is suppressed by approximately .
A spin-exchange relaxation-free comagnetometer is a promising high-precision gyroscope as its inertial measurement sensitivity can rival that of existing technologies. The magnetic field error is one of the main factors that limits the long-term stability of the comagnetometer. The steady-state response and frequency response models of a K-Rb-21Ne comagnetometer are modified by considering the spin-exchange rate between the electron spins and the nuclear spins. The modified models are used to redefine the bias magnetic sensitivity of the K-Rb-21Ne comagnetometer and the suppression method of low-frequency magnetic field error is proposed. We demonstrate the magnetic drift suppression method proposed in the article by optimizing the cell temperature and pump laser power density. This study is helpful to improve the rotation measurement performance of the K-Rb-21Ne comagnetometer.
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.
The atomic spin gyroscope (ASG), based on spin-exchange relaxation-free (SERF) co-magnetometers, is poised to become the next generation of high-precision inertial sensors. However, the long-term stability of the gyro can be limited by electron spin polarization. In this study, we investigate a novel real-time, in situ quantum feedback control technique for electron spin polarization in ASGs. By varying the pumping rates, we analyze the gyroscope’s response to the modulation magnetic field, finding that electron polarization dramatically affects the magnetic field response properties of ASGs. It’s demonstrated that the amplitude or phase of the electron spin resonance can be locked for in situ control of electron spin polarization in real-time. A K-Rb-21Ne co-magnetometer is established to implement the proposed method, where a transverse modulating magnetic field is applied to resonate with the electron spin. The lock-in amplification (LIA) technique is used to obtain the amplitude or phase of the electron spin resonance, and the electron spin polarization is closed-loop controlled by locking the second harmonic resonance amplitude or phase. The gyro signal is extracted from the first harmonic of the electron spin resonance. Our experimental results show that real-time in situ feedback control of electron spin significantly improves ASG’s long-term stability and suppresses low-frequency noise. This proposed method has broad application prospects, including optically pumped magnetometers (OPMs), nuclear magnetic resonance gyroscopes (NMRGs), and co-magnetometers.
Atomic spin sensors are essential for beyond-the-standard-model exploration, biomagnetic measurement, and quantum navigation. While the traditional DC mode spin-exchange relaxation-free (SERF) comagnetometer achieves ultrahigh sensitivity, further improvements require suppressing technical noise and surpassing standard quantum limit. In this work, we develop a K-Rb-21^{21}21Ne SERF atomic comagnetometer that dynamically polarizes the electron and nuclear spins, shielding signals from direct interference by pump light. We establish a three-phase evolutionary model for hybrid spin ensemble dynamics, yielding a complete analytical solution, and analyze the responses to various spin perturbations. Additionally, we achieve an averaged 38.5 %\%% suppression of the polarization noise and identify the key factors that limit sensitivity improvements. The dynamically polarized comagnetometer exhibits effective suppression of technical noise and holds the potential to overcome quantum noise limit, while offering promising applications in exploring new physics and precise magnetic field measurements.
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.
Atomic spin sensors are essential for beyond-the-standard-model exploration, biomagnetic measurement, and quantum navigation. While the traditional DC mode spin-exchange relaxation-free (SERF) comagnetometer achieves ultrahigh sensitivity, further improvements require suppressing technical noise and surpassing standard quantum limit. In this work, we develop a K-Rb- 21 Ne SERF atomic comagnetometer that dynamically polarizes the electron and nuclear spins, shielding signals from direct interference by pump light. We establish a three-phase evolutionary model for hybrid spin ensemble dynamics, yielding a complete analytical solution, and analyze the responses to various spin perturbations. Additionally, we achieve an average 39% suppression of the polarization noise and identify the key factors that limit sensitivity improvements. The dynamically polarized comagnetometer exhibits effective suppression of technical noise and holds the potential to overcome quantum noise limit while offering promising applications in exploring new physics and precise magnetic field measurements.