Entanglement of microwave-optical modes in a strongly coupled electro-optomechanical system

Changchun Zhong, Xu Han, Hong X. Tang, and Liang Jiang

Phys. Rev. A 101, 032345 – Published 26 March 2020

Abstract

Quantum transduction between microwaves and optics can be realized by quantum teleportation if given reliable microwave-optical entanglement, namely, entanglement-based quantum transduction. To realize this protocol, an entangled source with a high fidelity between the two frequencies is necessary. In this paper, we study microwave and optical entanglement generation based on a generic cavity electro-optomechanical system in the strong coupling regime. Splittings are shown in the microwave and optical output spectra and the frequency entanglement between the two modes is quantified. We show that entanglement can be straightforwardly encoded in the frequency-bin degree of freedom and propose a feasible experiment to verify entangled photon pairs. The experimental implementation is systematically analyzed, and the preferable parameter regime for entanglement verification is identified. An inequality is given as a criterion for good entanglement verification with analysis of practical imperfections.

Received 21 January 2020
Accepted 9 March 2020

DOI:https://doi.org/10.1103/PhysRevA.101.032345

Physics Subject Headings (PhySH)

Quantum entanglement Quantum information architectures & platforms Quantum networks

Quantum Information, Science & Technology

Authors & Affiliations

Changchun Zhong ^1,2,*, Xu Han^3,4, Hong X. Tang^2,4, and Liang Jiang ^1,2,†

¹Pritzker School of Molecular Engineering, University of Chicago, Chicago, Illinois 60637, USA
²Yale Quantum Institute, Yale University, New Haven, Connecticut 06520, USA
³Center for Nanoscale Materials, Argonne National Laboratory, Argonne, Illinois 60439, USA
⁴Department of Electrical Engineering, Yale University, New Haven, Connecticut 06520, USA

^*zhong.changchun@uchicago.edu
^†liang.jiang@uchicago.edu

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Vol. 101, Iss. 3 — March 2020

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Images

Figure 1
(a) Schematic of a piezo-optomechanical system with a blue-detuned laser drive. (b) The frequency landscape for the microwave, mechanical, and optical resonators and the pump laser. (c) The Gaussian unitary transformation connecting input and output mode operators. Take ${\vec{a}}_{in} = ({\hat{a}}_{in,c}, {\hat{a}}_{in,i})$ , and other vectors are similarly defined.
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Figure 2
Output power spectrum densities for (a) the optical mode and (c) the microwave mode, where mode splitting of $2 g_{em}$ appears when the ratio $R = κ_{e} / 4 g_{em}$ is decreased. The ratio $R = 1$ separates the weak and the strong coupling regimes. Dashed black lines in (a) and (c) correspond to the red (opt) and blue (mw) curves in (b) with the ratio $R = 0.2$ . In these plots, parameters from Table 1 are used and ${\bar{n}}_{ba} = 1$ , $C_{om} = 1$ .
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Figure 3
(a) $E_{F} (ω)$ with $ω = g_{em} = 2 π \times 2$ MHz (in the rotating frame) in terms of $C_{om}$ and the ratio $R = κ_{e} / 4 g_{em}$ . The dashed line separates the stable and unstable parameter regimes. (b) Entanglement rate for varied $C_{om}$ . The dashed vertical line is given by $R = 1$ , which separates the weak and the strong coupling regimes. In these plots, parameters in Table 1 are used and ${\bar{n}}_{ba} = 1$ .
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Figure 4
Schematic setup for detecting M-O Bell pairs encoded in the frequency-bin degree of freedom. The optical photon is analyzed with a balanced Mach-Zehnder interometer, composed of two 50:50 beam splitters (light blue), two narrow-band filters (short black line), a phase shifter ( $φ_{o}$ ), and a frequency shifter ( $f_{s}$ ). Two single-photon detectors are used in the end. Microwave photon detection is realized by cQED systems, where the microwave photon is converted into transmon qubit ( $Q_{1}$ or $Q_{2}$ ) excitation by Raman absorption, followed by a parity measurement, a cnot operation, a $π / 2$ rotation along the axis ( $sin φ_{e}, sin φ_{e}, 0$ ), and a high-fidelity single-qubit readout.
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Figure 5
(a) $S$ correlation curves in terms of the phase angle $φ_{e}$ with varied thermal baths, taking $R = κ_{e} / 4 g_{em} = 0.26$ and $C_{om} = 1$ . (b) “Phase diagram” for a CHSH inequality violation and a Bell-state fidelity larger than $1 / 2$ in the strong coupling regime with $R < 1$ . ${\bar{n}}_{ba} = 1$ .
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Figure 6
(a) Schematic of the M-O photon coincidence counting measurement. The microwave measurement repetition time is several microseconds, which includes the qubit preparation, operation, and Raman absorption time, which sets the detection time window $τ_{b}$ . (b) Second-order correlation function for three detection time resolutions, shown by the long-dashed blue, solid red, and short-dashed green lines. For these lines, we have $C_{om} = 1$ , $κ_{e,c} / κ_{e,i} = 20$ , and ${\bar{n}}_{ba} = 1$ . The dashed horizontal line is determined by $2 + ξ_{o} + ξ_{e} + ξ_{o} ξ_{e}$ .
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