Rydberg electromagnetically induced transparency in a large Hilbert space

Yongmei Xue, Liping Hao, Yuechun Jiao, Xiaoxuan Han, Suying Bai, Jianming Zhao, and Georg Raithel

Phys. Rev. A 99, 053426 – Published 30 May 2019

Abstract

We study Rydberg electromagnetically induced transparency (EIT) of cesium atoms in a magnetic field. The ladder level scheme consists of ground ( $6 S_{1 / 2}$ ), excited ( $6 P_{3 / 2}$ ), and Rydberg ( $48 D_{5 / 2}$ ) levels. The relevant 96 relevant magnetic sublevels are coupled to each other via coherent coupling and decay. A quantum Monte Carlo wave-function (QMCWF) approach is employed to solve the quantum master equation. The simulated EIT probe-absorption spectra and their magnetic-field dependence are compared with results of a cold-atom experiment, in which we perform an in situ, atom-based measurement of a rapidly decaying eddy-current magnetic field. The EIT spectrum in the magnetic field has two dominant lines with a Zeeman splitting of 5.6 MHz per gauss, which are employed to measure the magnetic field. The QMCWF results show good agreement with the experiment, exhibit additional spectroscopic features, and provide insights into the optical-pumping dynamics, radiation-pressure effects, and the relation of these phenomena with the EIT behavior.

Received 25 September 2018
Revised 28 March 2019

DOI:https://doi.org/10.1103/PhysRevA.99.053426

Physics Subject Headings (PhySH)

Atomic & molecular structure Zeeman effect

Atomic, Molecular & Optical

Authors & Affiliations

Yongmei Xue¹, Liping Hao¹, Yuechun Jiao^1,2, Xiaoxuan Han¹, Suying Bai¹, Jianming Zhao^1,2,*, and Georg Raithel^1,3

¹State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Laser Spectroscopy, Shanxi University, Taiyuan 030006, People's Republic of China
²Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan 030006, China
³Department of Physics, University of Michigan, Ann Arbor, Michigan 48109-1120, USA

^*Corresponding author: zhaojm@sxu.edu.cn

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Vol. 99, Iss. 5 — May 2019

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Images

Figure 1
Typical energy-level scheme. The 510 nm coupling laser drives the $| 6 P_{3 / 2} F^{'} = 5 〉 \to | 48 D_{5 / 2} 〉$ Rydberg transitions. The 852 nm probe laser is used to measure absorption on the $| 6 S_{1 / 2}, F = 4 〉 \to | 6 P_{3 / 2}, F^{'} = 5 〉$ transition. In the depicted case, a magnetic field pointing along $z$ splits the magnetic sublevels, and both coupling and probe lasers are linearly polarized along $x$ (transverse to the magnetic field). The arrows indicate the strongest transitions driven by the lasers. The numbers show Rabi frequencies (in MHz) for typical beam intensities used in our experiments.
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Figure 2
(a) Sketch of the experimental setup. Six beams of a 852 nm laser and the anti-Helmholtz coils constitute a cesium magneto-optical trap. 510 nm coupling and 852 nm probe laser beams are counterpropagated through the MOT cloud, probing the three-level Rydberg-EIT system. The probe beam is passed through a dichroic mirror (not shown), and the transmitted probe light is detected with a single-photon counting module (SPCM). When the MOT magnetic field is switched off, a transient eddy-current magnetic field is generated by currents induced in an aluminum plate located below the experimental chamber. A separate pair of Helmholtz coils is employed to superimpose an additional magnetic field over the eddy-current magnetic field. (b) Timing diagram. After turning off the MOT-coil current and the trapping beams, the Helmholtz coils are turned on at time $τ$ . To probe the magnetic field, Rydberg-EIT coupling and probe lasers are turned on for $100 μ s$ and scanned across the resonance.
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Figure 3
Measurements of the Rydberg ( $48 D_{5 / 2}$ ) EIT spectra for the indicated magnetic fields. Lorentzian fits of the EIT peaks are employed to measure EIT linewidths and line separations. As seen in (a), the fitted FWHM width of the EIT line at zero field is $γ_{EIT} / 2 π = 2.5$ MHz. The magnetic fields in (b) and (c) cause the EIT lines to Zeeman split into line pairs, resulting in the indicated peak-to-peak distances, $γ_{Z e e}$ . The gray solid lines show results of the quantum Monte Carlo wave-function model.
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Figure 4
Effect of scan duration in QMCWF results, for conditions that are otherwise identical with Fig. 3. The plot shows transmission spectra (left axis) and average $〈 m_{F, g} 〉$ (right axis) as a function of probe frequency for scan durations of $100 μ s$ (dashed) and 1 ms (solid). The magnitude of $〈 m_{F, g} 〉$ reveals the degree and the dynamics of optical pumping.
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Figure 5
Measurements (black filled circles) of Zeeman splitting, $γ_{Z e e}$ , as a function of magnetic field $B$ . The data are averages over three measurements. The red solid line is a linear fit to the data, showing that $γ_{Z e e} = B \times 5.65 MHz / G$ .
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Figure 6
Measurements of Zeeman splitting, $γ_{Z e e}$ , (a) and corresponding extracted magnetic field (b) as a function of delay time $τ$ . The splitting and the eddy-current magnetic field closely follow the indicated exponential fits, which have a characteristic decay time of $τ_{0} = 4.85 \pm 0.77$ ms.
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