Quantum interface between optics and microwaves with optomechanics

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.