Magneto-optical spectroscopy with arbitrarily polarized intensity-modulated light in $^{4}\mathrm{He}$ atoms

Magneto-optical spectroscopy with arbitrarily polarized intensity-modulated light in ${}^{4}{He}$ atoms

He Wang, Teng Wu, Haidong Wang, Xiang Peng, and Hong Guo

Phys. Rev. A 101, 063408 – Published 17 June 2020

Abstract

We present both a theoretical and experimental study of the magneto-optical spectra induced with intensity-modulated resonant laser light that synchronously pumps and detects the metastable ${}^{4}{He}$ atoms in the presence of a quasistatic magnetic field. We extend previous work and derive complete analytical expressions for the resonance signals by taking into account arbitrary magnetic-field directions and arbitrary light polarizations. The analytical results are derived by solving the Liouville equation using the irreducible tensor formalism on the assumption of low light power. We discuss the potential application of the derived analytical results in constructing and optimizing a dead-zone-free all-optical atomic magnetometer.

Received 17 March 2020
Accepted 28 May 2020

DOI:https://doi.org/10.1103/PhysRevA.101.063408

Physics Subject Headings (PhySH)

Magneto-optical spectra Optical pumping Zeeman effect

Atomic, Molecular & Optical

Authors & Affiliations

He Wang , Teng Wu , Haidong Wang , 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

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

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Vol. 101, Iss. 6 — June 2020

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Figure 1
Schematic of the experimental setup. A set of three-dimensional coils produces an arbitrarily oriented magnetic field $B$ . The metastable ${}^{4}{He}$ atoms exposed to the external magnetic field $B$ are enclosed in a glass cell, inside a five-layer $μ$ -metal magnetic shield. Resonant polarized light, propagating along the $Z$ axis, is used for optical pumping and probing. The fast axis of the quarter waveplate (QW) is fixed along the $X$ axis. A polarization beam splitter (PBS) and a half waveplate (HW) prepare linearly polarized light of adjustable orientation $α$ with respect to the $X$ axis. The ellipticity of the light polarization is determined by $α$ . An electro-optical modulator (EOM) is used to modulate the light intensity and is driven with a function generator (FG). A lock-in amplifier (LIA), whose reference signal (REF) comes from the FG, is used to extract the amplitude and the phase of the signal from the photodiode (PD).
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Figure 2
(a) Lowercase $x$ , $y$ , and $z$ form the magnetic-field coordinate system (black lines) and the capital $X$ , $Y$ , and $Z$ denote the light-field coordinate system (red or gray lines). Here $ϕ$ is the angle between the $Z$ and $z$ axes and $θ$ is the angle between the $Y$ axis and the projection of the $z$ axis on the $X − Y$ plane. (b) Magnetic sublevels of $2^{3} S_{1}$ and $2^{3} P_{0}$ in ${}^{4}{He}$ , with $σ_{\pm}$ - and $π$ -polarized components of a polarized light field with the quantization axis along the magnetic field $B$ . Here $μ = 1, 0, - 1$ are the $2^{3} S_{1}$ metastable sublevel indices and $m = 0$ is the $2^{3} P_{0}$ magnetic sublevel index.
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Figure 3
Amplitude (solid black line) and phase (dashed red line) signals demodulated by a lock-in amplifier at reference frequency $2 ω_{0}$ as a function of the frequency detuning $ω / 2 - ω_{0}$ .
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Figure 4
Experimental (dots) and theoretical (line) results for the normalized amplitudes (proportional to $f_{1}$ and $f_{2}$ ) of $ω_{0}$ (solid red lines) and $2 ω_{0}$ (dashed black lines) resonances versus the ellipticity of the light polarization. For each plot, the magnetic-field direction which is defined with $ϕ$ and $θ$ [see the definitions in Fig. 2] is different. The error bar shows the standard error of multiple readings, which is on the same scale as the symbol size. Since $θ$ has no effect on the signal amplitude when the light propagates along the magnetic field $B$ ( $ϕ = 0^{\circ}$ ), only one plot is given.
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Figure 5
The six contour plots based on the theoretical simulation results from Eqs. (A3) show the dependence of the resonance signal amplitudes on magnetic-field direction. The amplitudes of resonance signals are represented in percent of the maximum amplitude. (a) and (b) Ellipticity of the light polarization is adjusted to obtain the maximum amplitude of the resonance signal in each magnetic-field direction. (c) and (d) Circularly polarized light $α = 45^{\circ}$ . (e) and (f) Linearly polarized light $α = 0^{\circ}$ . (a) Only resonances at $2 ω_{0}$ are used. The minimum signal amplitude is 25% of the maximum. (b) Both resonances at $ω_{0}$ and $2 ω_{0}$ are used. The minimum signal amplitude is 64% of the maximum. (c) Only resonances at $2 ω_{0}$ are utilized and $ϕ = 0^{\circ}$ are dead zones. (d) Both resonances at $ω_{0}$ and $2 ω_{0}$ are utilized and $ϕ = 0^{\circ}$ are dead zones. (e) Only resonances at $2 ω_{0}$ are employed. Dead zones appear when both $ϕ$ and $θ$ equal $90^{\circ}$ . (f) Both resonances at $ω_{0}$ and $2 ω_{0}$ are employed. Dead zones occur when both $ϕ$ and $θ$ equal $90^{\circ}$ .
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Physical Review A

covering atomic, molecular, and optical physics and quantum information

Magneto-optical spectroscopy with arbitrarily polarized intensity-modulated light in ${}^{4}{He}$ atoms

He Wang, Teng Wu, Haidong Wang, Xiang Peng, and Hong Guo

Phys. Rev. A 101, 063408 – Published 17 June 2020

Abstract

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Physical Review A

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Magneto-optical spectroscopy with arbitrarily polarized intensity-modulated light in He4 atoms

He Wang, Teng Wu, Haidong Wang, Xiang Peng, and Hong Guo

Phys. Rev. A 101, 063408 – Published 17 June 2020

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Magneto-optical spectroscopy with arbitrarily polarized intensity-modulated light in ${}^{4}{He}$ atoms