Optical Measurements of Strong Microwave Fields with Rydberg Atoms in a Vapor Cell

D. A. Anderson, S. A. Miller, G. Raithel, J. A. Gordon, M. L. Butler, and C. L. Holloway

Phys. Rev. Applied 5, 034003 – Published 4 March 2016

Abstract

We present a spectral analysis of Rydberg atoms in strong microwave fields using electromagnetically induced transparency (EIT) as an all-optical readout. The measured spectroscopic response enables optical, atom-based electric-field measurements of high-power microwaves. In our experiments, microwaves are irradiated into a room-temperature rubidium vapor cell. The microwaves are tuned near the two-photon $65 D - 66 D$ Rydberg transition and reach an electric-field strength of $230 V / m$ , about 20% of the microwave-ionization threshold of these atoms. A Floquet treatment is used to model the Rydberg-level energies and their excitation rates. We arrive at an empirical model for the field-strength distribution inside the spectroscopic cell that yields excellent overall agreement between the measured and calculated Rydberg EIT-Floquet spectra. Using spectral features in the Floquet maps, we achieve an absolute strong-field measurement precision of 6%.

Received 15 October 2015

DOI:https://doi.org/10.1103/PhysRevApplied.5.034003

Physics Subject Headings (PhySH)

Electromagnetically induced transparency Radio frequency techniques

Rydberg atoms & molecules

Atomic, Molecular & Optical

Authors & Affiliations

D. A. Anderson^*, S. A. Miller, and G. Raithel

Department of Physics, University of Michigan, Ann Arbor, Michigan 48109, USA

J. A. Gordon, M. L. Butler, and C. L. Holloway

National Institute for Standards and Technology, U.S. Department of Commerce, Boulder, Colorado 80305, USA

^*Present address: Rydberg Technologies, LLC, Ann Arbor, Michigan 48104, USA.

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Vol. 5, Iss. 3 — March 2016

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Images

Figure 1
(a) Energy-level diagram for Rydberg EIT and the Rydberg states coupled by rf fields. (b) Illustration of the experimental setup showing the vapor cell, 480- and 780-nm laser beams (dashed lines), photodiode (PD), blue lens (LB), red lens (LR), dichroic mirror (DM), and microwave horn.
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Figure 2
Experimental spectra: (a) Weak-field measurement of 132.6495 GHz mm waves on the $26 D_{5 / 2} - 27 P_{3 / 2}$ one-photon transition versus $\sqrt{power}$ . Each spectrum is an average of 25 traces, and the signal is represented on a linear gray scale in arbitrary units. A calculated spectrum is overlaid with relative excitation rates from $5 P_{3 / 2}$ , given by the dot areas, and $E$ -field values on the top axis. (b) Strong-field measurement of 12.461 154 8 GHz microwaves on the $65 D - 66 D$ two-photon transition versus power. Each spectrum is an average of 20, and the signal is represented on a linear gray scale. The Floquet calculation is overlaid with excitation rates from $5 P_{3 / 2}$ , given by the dot areas, and $E$ -field values on the top axis. The background signal and additional features in the experimental strong-field spectrum are due to the microwave $E$ -field inhomogeneity within the cell (see Sec. 5).
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Figure 3
Calculated $| m_{j} | = 1 / 2$ (black circles) and $3 / 2$ (red circles) Floquet quasienergies and their relative excitation rates (circle area) from $5 P_{3 / 2}$ . The $E$ -field axis is scaled such that linear distance is proportional to intensity, allowing a comparison with the experimental map in Fig. 4. The region inside the black box corresponds to the parameter space covered in the experiment. The Floquet wave-packet dynamics for the levels marked 1, 2, and 3 are shown in Fig. 4. These calculations use a basis of all states with effective principal quantum number $56 \leq n^{*} \leq 73$ and orbital quantum number $ℓ \leq 10$ . The Floquet series are terminated at $N = \pm 8$ photon numbers.
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Figure 4
(a) Experimental spectra of the $65 D - 66 D$ two-photon transition versus microwave power. The signal is represented on a linear gray scale in arbitrary units. The arrows indicate coordinates that both correspond to the same avoided crossing in the theoretical Floquet map, marked 2 in Fig. 3. The solid arrow corresponds to the spatial region with the highest microwave intensity along the probe beam. The labels 1–5 mark the renderings of the same level in Fig. 3, observed in the five different intensity domains (see the text). (b) Composite Floquet map model of (a).
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