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Results in Physics

Bloch-Siegert shift under a bias magnetic field along arbitrary direction

Zhichao Ding, Weipeng Wang

Published Dec 12, 2024• 0 citations
Publisher

Abstract

In order to reduce the measuring error of magnetic resonance frequency caused by Bloch-Siegert shift, and improve the measurement accuracy of optical pumped alkali-metal magnetometers, the Bloch-Siegert shift is studied under a bias magnetic field in any direction. In this condition, the evolution equation of atomic spin is deduced. Based on the numerical solution of this equation, a method for extracting the Bloch-Siegert shift is proposed, which avoids the difficulty in achieving the analytical solution of the evolution equation. The numerical and analytical solutions of the evolution equation under special conditions are compared, verifying the rationality and necessity of using the numerical solution instead of approximate analytical solution to study the Bloch-Siegert shift under the bias magnetic field in any direction. By studying the Bloch-Siegert shift under different conditions, the typical conditions are selected and the Bloch-Siegert shift is numerically calculated when the bias magnetic field is in different directions. Through the analysis and verification of the calculation results, a theoretical model of the Bloch-Siegert shift under the bias magnetic field in any direction is obtained. This model is of great significance for correcting and reducing the measurement error of optical pumped alkali-metal magnetometers.

DOI
10.1016/j.rinp.2024.108085

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In order to reduce the measuring error of magnetic resonance frequency caused by Bloch-Siegert shift, and improve the measurement accuracy of optical pumped alkali-metal magnetometers, the Bloch-Siegert shift is studied under a bias magnetic field in any direction. In this condition, the evolution equation of atomic spin is deduced. Based on the numerical solution of this equation, a method for extracting the Bloch-Siegert shift is proposed, which avoids the difficulty in achieving the analytical solution of the evolution equation. The numerical and analytical solutions of the evolution equation under special conditions are compared, verifying the rationality and necessity of using the numerical solution instead of approximate analytical solution to study the Bloch-Siegert shift under the bias magnetic field in any direction. By studying the Bloch-Siegert shift under different conditions, the typical conditions are selected and the Bloch-Siegert shift is numerically calculated when the bias magnetic field is in different directions. Through the analysis and verification of the calculation results, a theoretical model of the Bloch-Siegert shift under the bias magnetic field in any direction is obtained. This model is of great significance for correcting and reducing the measurement error of optical pumped alkali-metal magnetometers.
We present investigations of radio-frequency (RF) resonances observed in an optically pumped rubidium vapor. By measuring the systematic shifts (the Bloch–Siegert shifts) of RF resonances in low magnetic fields, we demonstrate limitations of the rotating-wave approximation in the case of angular momentum F ≥ 1. The resonance shifts and deformations are characterized in a wide range of parameters and it is shown that the observed behavior is far more complex than in a standard two-level system. It is also demonstrated that the shifts can be controllably turned on or off by switching between the oscillating and rotating magnetic field. Experimental results are supported with numerical calculations, reproducing all features of the observed signals. Besides fundamental aspect of the research, application of rotating magnetic field helps to suppress/evaluate spectroscopic-measurement and precise-metrology systematic errors. The reported study has also important implications for quantum metrology and information processing beyond RWA and standard two-state qubit dynamics.
In this article, we analyze the amplitude-frequency and phase-frequency responses of a spin-exchange relaxation-free (SERF) atomic magnetometer with the nonorthogonal angle between the pump and probe beam. The optical nonorthogonality leads to a change in the photon spin direction of circularly polarized pump light, which decides the polarization direction of the atomic ensemble, causing significant differences in dynamic responses to the magnetic field. We theoretically analyze relationships between dynamic response solutions of the Bloch equation with different pump lights and magnetic field directions based on which the equations are linearized. The equations are solved with the Fourier transform method, and three-axis dynamic responses are obtained under the influences of optical nonorthogonality and residual static magnetic field. In the experiment, we verify the linear superposition characteristics between different response components. According to the results, we propose a novel method to quickly calibrate the nonorthogonal angle, which could reduce the optical nonorthogonal angle by 20 times, reaching 0.54°, and effectively enhance the dynamic magnetic field response signal in atomic magnetometers.
The light shift is an important error source for atomic magnetometers. It would vanish if the frequency of the circularly polarized light is tuned to the optical resonance center. For high-density alkali-metal atomic magnetometers, the vapor cell has a large optical depth near the resonance, resulting in the difficulty in obtaining the exact resonance center by measuring the optical absorption line. In order to solve this problem, we propose a method to tune the pump light to a frequency where the shift is minimum based on the magnetic field zeroing technique. In addition, we also compare our results with the fitting center of the optical absorption line based on the measurement data far detuned from the resonance. The experimental results show that our method achieves a better suppression result of the light shift.
We theoretically analyze an optically spin-polarized collection of atoms, which serves as a basis for atomic sensors. Assuming that the intrinsic atomic spin projection noise is negligible, we provide the closed-form autocorrelation function and the power spectral density (PSD) of the solution to a noisy version of an optically pumped Bloch equation, wherein each component of the external magnetic field is subjected to white noise. We conclude that noise in the bias B-field direction does not affect the autocorrelation function, up to first order in white noise covariance amplitudes. Moreover, the noise terms for the remaining two axes make different contributions to the magnetic noise-driven spin PSD; in particular, the contribution corresponding to noises perpendicular to the probing direction dominates at high frequencies. Some results concerning the second (and higher)-order terms are given. In particular, we anticipate a decrease in the effective Larmor frequency despite an increase in the magnetic field magnitude in the case of anisotropic transversal B-field noises. The analytic results are supported by Monte Carlo simulations employing the Euler–Maruyama method. The analytic methodology is applied to the case of a Bell–Bloom magnetometer, which reveals a non-linearity in the PSD of the magnetometer output and also a broadening effect due to magnetic field noise.
This paper investigates the performance optimization of optically pumped magnetometers under zero-field parametric modulation. Based on the analytical solutions of the Bloch equation, both longitudinal and transverse modulations are studied experimentally. To estimate the nonuniform polarization distribution of alkali-metal atoms in the vapor cell, an average pumping rate model is proposed. Furthermore, the accuracy of this model and the measurement of the transverse relaxation rate are verified via the agreement between experimental and theoretical values. The results indicate that optimal performance can be achieved by employing a suitable modulation field, the selection of which is related to the modulation index uuu in the Bessel series and the pump-light intensity. Although both operating modes show similar responses to weak magnetic fields, their effects on pump-light intensity are different due to the means of detecting atomic polarization. An optimal value of the pump-light intensity on the response strength exists in longitudinal modulation. However, with regard to transverse modulation, the sensitivity under weak pump-light intensity is better. This research has far-reaching significance for cases when the parametric modulation is manipulated.
Subject of study. Magnetic resonance frequency shifts caused by spin exchange collisions involving optically oriented alkali atoms in the ground state are studied. Aim of study. Spin-exchange collisions involving optically oriented pairs of alkali atoms of different types are theoretically studied to determine the shifts in the magnetic resonance line frequencies as a function of temperature for various pairs of alkali atoms under various optical orientation conditions in order to determine optimum constraints for the construction of quantum magnetometers with optical pumping using mixtures of alkali atoms. Method. Collisions between optically oriented alkali atoms are analyzed within the framework of quantum scattering theory, and data on the interaction potentials of alkali-atom dimers are used to calculate the scattering phases for collisions involving these potentials and the imaginary parts of the complex spin-exchange cross-section. The resulting cross sections as a function of energy were used to determine the magnetic resonance frequency shifts as a function of temperature. Main results. The magnetic resonance line frequency shifts for the following pairs of alkali atoms were obtained as a function of temperature: 39K−133Cs, 39K−85Rb, and 133Cs−85Rb. The shift in the magnetic resonance line involving the F=1 hyperfine state for a 39K−85Rb alkali-atom pair was found to pass through zero near temperature 480 K. Practical significance. The results obtained in this paper can be used to develop zero-spin-exchange-shift quantum electronic devices based on the optical orientation of atoms. In particular, it is possible to develop co-magnetometers based on the optical orientation of alkali atoms.