Cavity quantum electro-optics. II. Input-output relations between traveling optical and microwave fields

TL;DR

This paper develops input-output relations for a cavity electro-optic modulator, enabling efficient microwave-to-optical photon conversion and entanglement generation, bridging circuit QED and quantum optics.

Contribution

It derives the quantum input-output relations for traveling optical and microwave fields coupled via a cavity electro-optic modulator, highlighting conditions for efficient conversion and entanglement.

Findings

Microwave photons can be coherently up-converted to optical photons with unit efficiency.

The modulator acts as a nondegenerate parametric amplifier under blue-sideband pumping.

The relations resemble a beam splitter for traveling fields in ideal conditions.

Abstract

In the previous paper [M. Tsang, Phys. Rev. A 81, 063837 (2010), e-print arXiv:1003.0116], I proposed a quantum model of a cavity electro-optic modulator, which can coherently couple an optical cavity mode to a microwave resonator mode and enable novel quantum operations on the two modes, including laser cooling of the microwave mode, 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 a 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.