On-chip microwave-to-optical quantum coherent converter based on a superconducting resonator coupled to an electro-optic microresonator

C. Javerzac-Galy, K. Plekhanov, N. R. Bernier, L. D. Toth, A. K. Feofanov, and T. J. Kippenberg

Phys. Rev. A 94, 053815 – Published 9 November 2016; Erratum Phys. Rev. A 98, 069902 (2018)

Abstract

We propose a device architecture capable of direct quantum coherent electro-optical conversion of microwave-to-optical photons. The hybrid system consists of a planar superconducting microwave circuit coupled to an integrated whispering-gallery-mode microresonator made from an electro-optical material. We show that by exploiting the large vacuum electric field of the planar microwave resonator, electro-optical (vacuum) coupling strengths $g_{0}$ as large as $\sim 2 π O (10 - 100)$ kHz are achievable with currently available technology—a more than 3 orders of magnitude improvement over prior designs and realizations. Operating at millikelvin temperatures, such a converter would enable high-efficiency conversion of microwave-to-optical photons. We analyze the added noise and show that maximum quantum coherent conversion efficiency is achieved for a multiphoton cooperativity of unity which can be reached with optical power as low as $O (1)$ mW.

Received 23 December 2015

DOI:https://doi.org/10.1103/PhysRevA.94.053815

Physics Subject Headings (PhySH)

Cavity quantum electrodynamics Hybrid quantum systems Optomechanics Superconducting qubits

Quantum Information, Science & TechnologyAtomic, Molecular & Optical

Erratum

Erratum: On-chip microwave-to-optical quantum coherent converter based on a superconducting resonator coupled to an electro-optic microresonator [Phys. Rev. A 94, 053815 (2016)]

C. Javerzac-Galy, K. Plekhanov, N. R. Bernier, L. D. Toth, A. K. Feofanov, and T. J. Kippenberg

Phys. Rev. A 98, 069902 (2018)

Authors & Affiliations

C. Javerzac-Galy, K. Plekhanov, N. R. Bernier, L. D. Toth, A. K. Feofanov^*, and T. J. Kippenberg^†

École Polytechnique Fédérale de Lausanne (EPFL), Institute of Physics, CH-1015 Lausanne, Switzerland

^*alexey.feofanov@epfl.ch
^†tobias.kippenberg@epfl.ch

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Issue

Vol. 94, Iss. 5 — November 2016

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Images

Figure 1
Principle for a cavity electro-optical system for microwave-to-optical conversion, composed of (a) a $χ^{(2)}$ WGM microresonator (in blue), resonant at $ω_{a}$ coupled to a waveguide with an external coupling rate $κ_{a}^{(ex)}$ and an intrinsic loss rate $κ_{a}^{(in)}$ , and an LC microwave circuit, resonant at $ω_{b}$ coupled via a feedline (here capacitively coupled) with an external coupling rate $κ_{b}^{(ex)}$ . The distance between the microwave resonator electrodes is denoted by $d$ , and $l$ is the length of the optical path. (b) In the resolved sideband limit the system enables via lower sideband pumping at $ω_{p} = ω_{a} - ω_{b}$ to laser cool the microwave photons, i.e., up-convert them to the cold optical mode, establishing a coherent interface between microwave and optical fields. To minimize the required optical input power it is advantageous to make the lower sideband coincide with another resonant optical cavity mode so that their free spectral range (FSR) matches the microwave resonant frequency $ω_{b}$ .
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Figure 2
Schematic view of the cavity quantum electro-optical system proposed for up-converting microwave photons to the optical domain. Panel (a) depicts the top view and panel (b) shows a sample cross section. The optical cavity is a microring resonator made out of z-cut ${LiNbO}_{3}$ coupled via a waveguide by evanescent-field coupling. The microwave cavity is an open $\frac{λ}{2}$ microstrip resonator. The resonator is overlapped with the optical microring to maximize the mode overlap and thus the electro-optic coupling. Note that the symmetry of the microwave resonator needs to be broken to achieve electro-optical coupling, for example, by grounding its ends, to ensure that only the positive phase of the microwave electric field profile couples to the optical microresonator. The microwave cavity is capacitively coupled to a microstrip feedline.
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Figure 3
2D FEM simulations of an optimized geometry. (a) Optical energy density profile of an optical WGM mode in a lithium niobate resonator with $ω_{a} = 2 π \times 200 THz$ . The refractive index contrast between the ${LiNbO}_{3}$ WGM and the surrounding ${SiO}_{2}$ provides high confinement of the optical energy. (b) Electric potential and electric field (arrows) across the electrodes inside the microwave cavity at $ω_{b} = 2 π \times 6 GHz$ . Direction and amplitude of the field are optimized to maximize $g_{0}$ . The distance between the electrodes is designated by $d$ . Plots are on log scale with a color map given on the right in arbitrary units.
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