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Photonic Sensors

A Coil Constant Calibration Method Based on the Phase-Frequency Response of Alkali Atomic Magnetometer

Han Yao, Danyue Ma, Junpeng Zhao, Jixi Lu, Ming Ding

Published Jan 18, 2019• 9 citations
Publisher

Abstract

We propose an in-situ method to calibrate the coil constants of the optical atomic magnetometer. This method is based on measuring the Larmor precession of spin polarized alkali metal atoms and has been demonstrated on a K-Rb hybrid atomic magnetometer. Oscillation fields of different frequencies are swept on the transverse coil. By extracting the resonance frequency through phase-frequency analysis of electron spin projection, the coil constants are calibrated to be 323.1 ± 0.28 nT/mA, 108 ± 0.04 nT/Ma, and 185.8 ± 1.03 nT/mA along the X , Y , and Z directions, respectively.

DOI
10.1007/s13320-019-0530-4

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We propose an in-situ method to calibrate the coil constants of the optical atomic magnetometer. This method is based on measuring the Larmor precession of spin polarized alkali metal atoms and has been demonstrated on a K-Rb hybrid atomic magnetometer. Oscillation fields of different frequencies are swept on the transverse coil. By extracting the resonance frequency through phase-frequency analysis of electron spin projection, the coil constants are calibrated to be 323.1 ± 0.28 nT/mA, 108 ± 0.04 nT/Ma, and 185.8 ± 1.03 nT/mA along the X , Y , and Z directions, respectively.
An in situ simultaneous measurement of magnetic coil constants and nonorthogonal angles method is proposed using the atomic magnetometer. Based on the transient response of the atomic spin polarization under the different magnetic fields, we establish the corresponding measurement model of magnetic coil constants and nonorthogonal angles through the relationship between the Larmor precession frequency and the external magnetic field. By this model, we experimentally obtained the coil constants of x , y, and z axes are, respectively, 9.04 ± 0.10, 8.94 ± 0.07, and 4.34 ± 0.02 nT / V in our system. The nonorthogonal angles are 89.04 deg between x axis and y axis, 88.60 deg between y axis and z axis, and 91.15 deg between z axis and x axis. This method can be used to simultaneously measure magnetic coil constants and nonorthogonal angles without relying on external instruments, which provides a basic guarantee for the accurate calculation sensitivity of spin-exchange-relaxation-free atomic magnetometers, especially for miniaturized atomic magnetometers.
The calibration results of the triaxial coils affect the atomic magnetometer’s measurement sensitivity. For precise in situ calibration, we first studied the transient atomic dynamics of a dual-beam spin-exchange relaxation free (SERF) atomic magnetometer under alternating magnetic fields. We obtained the corresponding dynamic free-induction-decay (FID) curves by alternately applying square wave signals to thex{x}x-,y{y}y-, andz{z}z-axis coil, and then extracted the precession frequencies by fast Fourier transform (FFT) to achieve a decoupled calibration of the triaxial coil constants. Our calibration results were in better agreement under different experimental conditions than traditional parameter fitting methods with a relative error of less than 1.5% compared to conventional fluxgate calibration methods. Furthermore, we simultaneously measured nonorthogonal angles between each pair of axes: x–y, y–z, and z–x, respectively, which are used to correct the magnetic fields error. This method is suitable for coil calibration and nonorthogonal correction of integrated and miniaturized dual beam magnetometers.
Abstract The alkali number density inside the sealed vapor cell restricts the fundamental sensitivity of the atomic magnetometer and may decrease in the long term, thus motivating the investigation of an in situ density determination method on atomic magnetometers. This paper presents a method to measure the alkali number density, which is proportional to the spin-exchange relaxation rate, through phase-frequency analysis. The magnetic resonance response of the atomic magnetometer was actively strengthened at low polarization by increasing the oscillating field amplitude. To downplay the side effect of the transverse field broadening, phase-frequency analysis was applied to extract the transverse relaxation time limited by spin-exchange collisions. The experimental results coincided well with the saturated vapor pressure curve ranging from 413 K to 463 K. Calculated densities were approximately 0.779–0.992 times those of predictions. The density measurement accuracy was improved compared to traditional methods.
In this paper, we experimentally study transient dynamics of spin polarized atoms in the spin-exchange-relaxation-free (SERF) regime with a single-beam configuration. We pumped atoms with a weak detuning pumping beam, along with a sequence of magnetic field pulses orthogonal to the pumping beam were applied. The dynamics of atomic spin, which experiences Larmor precession under the perturbation of magnetic field, is detected by the transmitted pumping beam. Benefited from the long coherence time of atomic spin in the SERF regime, the dependence of precession frequency and decay rate, which is equal to the magnetic resonance linewidth of atomic spin, on magnetic fields is studied with the transient dynamics of atomic spin in the limit of low spin polarization. Moreover, we demonstrate that coil constants can be calibrated by analyzing the precession frequency of the transient dynamics of atomic spin. And the experimental results show that the coil constants are 114.25 ± 0.02 nT/mA and 114.12 ± 0.04 nT/mA in x- and y-axis, respectively. This method is particularly applicable to study the atomic spin dynamics and calibrate the coil constant in situ of a miniature single-beam SERF magnetometer.
This paper presents a method for measuring the spin polarization of spin-exchange relaxation-free (SERF) atomic magnetometers at extremely large optical depths. Owing to the slowing-down effect, the spin polarization can be extracted by measuring the slowing-down factor extracted from the precession frequency. However, this technique is limited by a significant error in the regime of extremely large optical depths, where the pump beam intensity for achieving the optimized spin polarization of alkali atoms is significantly increased. We observed that the instantaneous precession frequency measured in the regime where the spin-exchange rate is not much larger than the Larmor frequency was no longer a constant but varied with the pump beam intensity. Thus, a method for measuring spin polarization based on the ratio of the precession frequency to the measured instantaneous precession frequency is proposed. Based on the proposed method, the spin polarization at a temperature of 473K and optical depth of 64 is measured. The measurement results were accordant with theoretical analysis. The expanded uncertainties of the experimental results varied between 1.8% and 9.6%. The proposed method is also applicable to other atomic devices operated in the SERF regime with extremely large optical depths, such as co-magnetometers and atomic spin gyroscopes.
We report a rubidium atomic magnetometer based on pump-probe nonlinear magneto-optical rotation. The rubidium vapor cell is placed in a five-layer magnetic shield with inner coils that can generate uniform magnetic fields along the direction of pump beam, and the cell is also placed in the center of a Helmholtz coil that can generate an oscillating magnetic field perpendicular to the direction of pump beam. The atoms are optically pumped by circularly polarized pump beam along a constant magnetic field in a period of time, then the pump beam is turned off and a /2 pulse of oscillating magnetic field for 87Rb atoms is applied. After the above process, the individual atomic magnetic moments become phase coherent, resulting in a transverse magnetization vector precessing at the Larmor frequency in the magnetic field. The linearly polarized probing beam is perpendicular to the direction of magnetic field, and can be seen as a superposition of the left and right circularly polarized light. Because of the different absorptions and dispersions of the left and right circularly polarized light by rubidium atoms, the polarization direction of probing beam rotates when probing beam passes through rubidium vapor cell. The rotation of the polarization is subsequently converted into an electric signal through a polarizing beam splitter. Finally, the decay signal related to the transverse magnetization vector is measured. The Larmor frequency proportional to magnetic field is obtained by the Fourier transform of the decay signal. The value of magnetic field is calculated from the formula:B=(2/) f, where and f are the gyromagnetic ratio and Larmor frequency, respectively. In order to measure the magnetic field in a wide range, the tracking lock mode is proposed and tested. The atomic magnetometer can track the magnetic field jump of 1000 nT or 10000 nT, indicating that the atomic magnetometer has strong locking ability and can be easily locked after start-up. The main performances in different magnetic fields are tested. The results show that the measurement range of the atomic magnetometer is from 100 nT to 100000 nT, the extreme sensitivity is 0.2 pT/Hz1/2, and the magnetic field resolution is 0.1 pT. The transverse relaxation times of the transverse magnetization vector in different magnetic fields are obtained, and the relaxation time decreases with the increase of the magnetic field. When the measurement range is from 5000 nT to 100000 nT, the magnetic field sampling rate of the atomic magnetometer can be adjusted in a range from 1 Hz to 1000 Hz. The atomic magnetometer in high sampling rate can measure weak alternating magnetic field at low frequency. This paper provides an important reference for developing the atomic magnetometer with large measurement range, high sensitivity and high sampling rate.