Atomic spin-exchange collisions in magnetic fields

Wei Xiao, Teng Wu, Xiang Peng, and Hong Guo

Phys. Rev. A 103, 043116 – Published 22 April 2021

Abstract

Spin-exchange collisions among alkali-metal atoms affect the coherence time and gyromagnetic ratio of atoms by redistributing the ground-state population. We theoretically study the interactions between magnetic fields and atoms in the presence of spin-exchange collisions. Using the modified Bloch equations derived from the density-matrix equation in a low spin-polarization limit, we obtain explicit formulas describing the role of spin-exchange collisions in the interactions between atoms and magnetic fields, especially the nonresonant radio-frequency fields, which are widely used to manipulate atoms. The results derived from these equations agree well with density-matrix simulations and previous experimental results, and provide a simple and precise way to quantitatively analyze the effect of spin-exchange collisions on atoms. Our paper is helpful to gain physical insight into the spin-exchange collisions and optimize the performance of atom-based precision measurement instruments.

Received 10 August 2020
Revised 21 March 2021
Accepted 24 March 2021

DOI:https://doi.org/10.1103/PhysRevA.103.043116

Physics Subject Headings (PhySH)

Atomic & molecular collisions Zeeman effect

Precision measurements

Atomic, Molecular & Optical

Authors & Affiliations

Wei Xiao , Teng Wu ^*, Xiang Peng , and Hong Guo ^†

State Key Laboratory of Advanced Optical Communication Systems and Networks, Department of Electronics, and Center for Quantum Information Technology, Peking University, Beijing 100871, China

^*wuteng@pku.edu.cn
^†hongguo@pku.edu.cn

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Issue

Vol. 103, Iss. 4 — April 2021

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Images

Figure 1
(a) The simulated (diamonds and circles) and analytical (solid red line and dashed blue line) SE relaxation rate caused by the rf field modulated at 50 and 2 kHz, respectively, where $R_{SE} / 2 π = 13$ kHz. (b) The simulated (diamonds) SE relaxation rate and analytical (lines) SE relaxation rate calculated by using Eqs. (15b) and (16).
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Figure 2
(a) The SE relaxation rate in two different cases, where a static field ( $B_{0} = 20$ nT) is applied parallel and perpendicular to the rf field ( $B_{1} = 200$ nT, $ω / 2 π = 2$ kHz), respectively. The analytical results (lines) agree with the density-matrix simulations (diamonds and circles). (b) The ratio between the effective precession frequency $ω_{eff}$ and the free atomic Larmor frequency $ω_{0}$ as a function of the SE rate $R_{SE}$ . The simulated data are taken for $B_{0} = 20$ nT and $ω / 2 π = 2$ kHz at different rf field cases, including $B_{1} = 0$ (solid red line), a parallel rf field with the amplitude of 100 nT (dashed pink line), a perpendicular rf field with the amplitude of 100 nT (dash-dotted green line) and 200 nT (dotted orange line), respectively, and a perpendicular corotating field with the amplitude of 60 nT (dash-dotted blue line).
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Figure 3
(a) The equivalent magnetic fields ${\tilde{B}}_{a}$ and ${\tilde{B}}_{b}$ in the rotating coordinate system. Another new coordinate system is set by the parallel $y^{'}$ axis and ${\tilde{B}}_{a}$ . (b) The dependencies of the simulated (diamonds) and theoretical (red line) effective Rabi frequency $Ω_{a}^{eff}$ on the angle between the two equivalent magnetic fields ${\tilde{B}}_{a}$ and ${\tilde{B}}_{b}$ in the SERF regime. (c) The dependencies of the effective Rabi frequency $Ω_{a}^{eff}$ on the SE rate in different angles $θ = 0, π / 8, π / 4$ . The data are taken with the field modulation amplitude $B_{1} = 60$ nT and modulation frequency $ω / 2 π = 2$ kHz.
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Figure 4
The SE collision broadening of Hanle resonance linewidth as a function of the SE rate, and the simulated (diamonds) linewidth and analytical (lines) linewidths calculated by using Eqs. (15b) and (16), where $R_{OP} / R_{SD} = 0.1$ .
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Figure 5
(a) The dependence of the linewidth of magnetic resonance on the bias magnetic field for several values of the polarization. (b) The dependence of the linewidth of magnetic resonance on the polarization for several values of the magnetic field. (c) The normalized effective Larmor frequency $ω_{eff} / ω_{0}$ as a function of the bias magnetic field for several values of the polarization. (d) The normalized effective Larmor frequency $ω_{eff} / ω_{0}$ as a function of the polarization for several values of the magnetic field. The analytical results based on Eqs. (32a) and (32b) show good consistency with DME simulations.
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