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Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)

Quantum interface between optics and microwaves with optomechanics

Sh. Barzanjeh, Mehdi Abdi, Gerard J Milburn, P. Tombesi, David Vitali

Published May 1, 2013• 1 citation

Abstract

A number of schemes for a quantum interface between light at different wavelengths have been demonstrated and very recently various solutions for interfacing optics and microwaves have been proposed. We describe here a reversible quantum interface between optical and microwave photons based on a micro-mechanical resonator in a superconducting circuit, simultaneously interacting with an optical and a microwave cavity. When the cavities are appropriately driven, the mechanical resonator mediates an effective parametric amplifier interaction, entangling an optical signal and a microwave idler. Such continuous variable (CV) entanglement can be then exploited to implement CV teleportation. The optical output is mixed with an optical `client' field in an unknown quantum state on a beam splitter at the transmitting site (Alice). The two outputs are then subject to homodyne detection and the classical measurement results communicated to the receiving site (Bob). Upon receipt of these results, Bob makes a conditional displacement of the microwave field, again using beam splitters and a coherent microwave source. The resulting state of the output microwave field is then prepared in the same quantum state as the optical input state. The process is entirely symmetric: the Alice and Bob roles can be exchanged and an unknown input microwave field can be teleported onto the optical output field at Alice, realising therefore a reversible quantum state transfer between fields at completely different wavelengths.

DOI: 10.1109/cleoe-iqec.2013.6801643

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We describe a reversible quantum interface between an optical and a microwave field using a hybrid device based on their common interaction with a micromechanical resonator in a superconducting circuit. We show that, by employing state-of-the-art optoelectromechanical devices, one can realize an effective source of (bright) two-mode squeezing with an optical idler (signal) and a microwave signal, which can be used for high-fidelity transfer of quantum states between optical and microwave fields by means of continuous variable teleportation.

We propose a scheme for entangling the optical and microwave output modes of the respective cavities by using a micro mechanical resonator. The micro-mechanical resonator on one side is capacitively coupled to the microwave cavity and on the other side is coupled to a high finesses optical cavity. We then show how this continuous variable entanglement can be profitably used to teleport the non-Gaussian number state |1> and the superposition (|0>+|1>)/\surd2 from the microwave cavity output mode onto an output of optical cavity mode with fidelity much larger than the no-cloning limit.

In a previous paper [Phys. Rev. A 81, 063837 (2010)], I proposed a quantum model of the cavity electro-optic modulator, which can coherently couple an optical cavity mode to a microwave resonator mode and enable quantum operations on the two modes, including laser cooling of the microwave resonator, electro-optic entanglement, and backaction-evading optical measurement of a microwave quadrature. In this sequel, I focus on the quantum input-output relations between traveling optical and microwave fields coupled to the cavity electro-optic modulator. With red-sideband optical pumping, the relations are shown to resemble those of a beam splitter for the traveling fields, so that in the ideal case of zero parasitic loss and critical coupling, microwave photons can be coherently up converted to ``flying'' optical photons with unit efficiency, and vice versa. With blue-sideband pumping, the modulator acts as a nondegenerate parametric amplifier, which can generate two-mode squeezing and hybrid entangled photon pairs at optical and microwave frequencies. These fundamental operations provide a potential bridge between circuit quantum electrodynamics and quantum optics.

State transfer between light and microwaves is a key challenge in quantum networks. Promising transducers use a mechanical intermediary that couples to both fields via radiation pressure. Such electro-optomechanical devices have achieved high efficiencies, yet require resolved-sideband cavities, and generally compromise in scalability and noise performance. Here, we relax this constraint by extending the protocol of Navarathna et al. that transfers optical quantum information onto a mechanical resonator using a broadband, sideband-unresolved cavity and feedback. Combining this with parametric mechanical-to-microwave conversion, we show that continuous optical-to-microwave quantum state transfer is possible using measurement-based feedback, while all-optical coherent feedback enables bidirectional transfer. To assess the transfer, we introduce the quantum transfer witness

\mathcal{W}_T

, which -- though similar to the input-referred added noise -- also identifies whether a channel is capable of both preserving Gaussian entanglement and outperforming classical transduction schemes. Finally, we show that quantum-compatible noise performance is within reach of current experimental capabilities. Our results unlock a new design space for electro-optomechanical transducers and strengthens their candidacy as scalable quantum links between distant nodes.

Generating usable output-entanglement in continuous variable systems can serve as a viable resource for improving applications in quantum information science. In this work, we show how to generate steady-state output-entanglement in a two-stage conversion setup between optical and microwave photon which employs resonantly coupled magnetic and mechanical excitations, as proposed in Phys. Rev. Applied 18, 044059 (2022). We show that the entanglement can be maximized for the same set of parameters which optimize the frequency-conversion efficiency, and that it can be leveraged for a teleportation-based state-transfer protocol for coherent input-states with fidelity close to unity. We propose an implementation based on an Yittrium Iron Garnet disk of micrometer scale, and use both simulation results and reasonable estimates to assess the performance under optimized conditions. We find a maximum teleportation fidelity of

0.75

for the proposed setup.

We propose a scheme for entangling the optical and microwave output modes of the respective cavities by using a micro mechanical resonator. The micro-mechanical resonator on one side is capacitively coupled to the microwave cavity and on the other side is coupled to a high finesses optical cavity. We then show how this continuous variable entanglement can be profitably used to teleport the non-Gaussian number state |1> and the superposition (|0>+|1>)/\surd2 from the microwave cavity output mode onto an output of optical cavity mode with fidelity much larger than the no-cloning limit.