Quantum transducer in circuit optomechanics

Mechanical resonators are macroscopic quantum objects with great potential. They couple to many different quantum systems such as spins, optical photons, and Bose Einstein condensates. It is difficult to measure and manipulate a phonon state due to the tiny motion in the quantum regime. On the other hand, microwave resonators are powerful quantum devices since arbitrary photon states can be synthesized and measured with the quantum tomography. We show that linear coupling, strong and controlled with gate voltage, between mechanical and microwave resonators enables creation of quantum phonon states, manipulation of hybrid entanglement between phonons and photons, and generation of entanglement between two mechanical oscillators. In circuit quantum optomechanics, the mechanical resonator acts as a quantum transducer between an auxiliary quantum system and the microwave resonator, which is used as a quantum bus. As an example, we demonstrate how two mechanical resonators coupled to one microwave resonator and two spins can facilitate entanglement generation between the spins.