Microwave-to-optical conversion via four-wave mixing in a cold ytterbium ensemble

Jacob P. Covey, Alp Sipahigil, and Mark Saffman

Phys. Rev. A 100, 012307 – Published 8 July 2019

Abstract

Interfacing superconducting qubits with optical photons require noise-free microwave-to-optical transducers, a technology currently not realized at the single-photon level. We propose to use four-wave mixing in an ensemble of cold ytterbium (Yb) atoms prepared in the metastable “clock” state. The parametric process uses two high-lying Rydberg states for bidirectional conversion between a 10 GHz microwave photon and an optical photon in the telecommunication E-band. To avoid noise photons due to spontaneous emission, we consider continuous operation far detuned from the intermediate states. We use an input-output formalism to predict conversion efficiencies of $\approx 50 %$ with bandwidths of $\approx 100$ kHz.

Received 19 April 2019

DOI:https://doi.org/10.1103/PhysRevA.100.012307

Physics Subject Headings (PhySH)

Hybrid quantum systems Quantum optics

Atomic, Molecular & OpticalQuantum Information, Science & Technology

Authors & Affiliations

Jacob P. Covey ^1,*, Alp Sipahigil², and Mark Saffman³

¹Division of Physics, Mathematics and Astronomy, California Institute of Technology, Pasadena, California 91125, USA
²Thomas J. Watson, Sr., Laboratory of Applied Physics, California Institute of Technology, Pasadena, California 91125, USA
³Department of Physics, University of Wisconsin-Madison, 1150 University Avenue, Madison, Wisconsin 53706, USA

^*covey@caltech.edu

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Vol. 100, Iss. 1 — July 2019

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Images

Figure 1
Conversion loop. The atom is initialized in the $6 s 6 p^{3} P_{0}$ “clock” state ( $| 1 〉$ ). This state is in a loop of three other states which include the $6 s 60 s^{3} S_{1}$ Rydberg state ( $| 2 〉$ ), the $6 s 60 p^{3} P_{0}$ Rydberg state ( $| 3 〉$ ), and the $6 s 5 d^{3} D_{1}$ state ( $| 4 〉$ ). The two Rydberg states $| 2 〉$ and $| 3 〉$ are spaced by 10.1 GHz and strongly coupled by an electric dipole moment. The states $| 4 〉$ and $| 1 〉$ are separated by a telecom-band photon with wavelength $λ_{o} = 1389$ nm. We consider continuous wave operation in which the coupling fields are detuned from the intermediate states. The population primarily resides in $| 1 〉$ .
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Figure 2
Transduction circuit in a cryogenic environment. (a) The copper microwave resonator with round capacitor plates on conically tapered pillars (not to scale). The red beams show the optical dipole trapping of the cigar-shaped cloud (green). (b) The cryogenic environment with transduction circuit inside. The black box shows the cryostat surfaces and the blue shows the viewports for the optical fields, which can be combined using a dichroic mirror. A traveling microwave photon in mode $b_{in} (t)$ from an external superconducting circuit enters the microwave resonator (orange) containing the atomic cloud (green ellipse). The UV (purple) and blue (blue) driving fields and the telecommunication-wavelength cavity mode (red) are coaxial to obtain phase matching in the atomic medium. (c) A zoom-in of the microwave resonator plates and the atomic ensemble, shown on the $y z$ plane and the $x y$ plane. Simulated root-mean-square (RMS) electric-field magnitude per single photon shown on the $y z$ plane (d) and $x y$ plane (e). The vector field between the resonator plates is shown in (e). The field amplitude and orientation is uniform across the atomic cloud.
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Figure 3
Impedance matching and bandwidth. (a) The conversion efficiency $η (ω = 0)$ as a color plot ranging from 0.0 to $≲ 0.6$ . It is shown as a function of the mode filling fraction $F$ on the vertical axis and the $Q$ - factor of the microwave resonator on the horizontal axis. The thick black dot corresponds to the proposed values in this work. (b) The conversion efficiency $η (ω)$ as a function of frequency $ω$ . The three colors correspond to $Q_{μ} = 1 \times 10^{3}$ (blue, bottom), $Q_{μ} = 2 \times 10^{3}$ (orange, middle), and $Q_{μ} = 4.5 \times 10^{3}$ (green, top). We focus on the case of $Q_{μ} = 4.5 \times 10^{3}$ throughout [which corresponds to the black dot in (a)], for which the FWHM bandwidth is $\approx 100$ kHz.
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