Mechanical resonators are macroscopic quantum objects with great potential. They couple to many different quantum systems such as spins, optical photons, cold atoms, and Bose Einstein condensates. It is however difficult to measure and manipulate the phonon state due to the tiny motion in the quantum regime. On the other hand, microwave resonators are powerful quantum devices since arbitrary photon state can be synthesized and measured with a quantum tomography. We show that a linear coupling, strong and controlled with a gate voltage, between the mechanical and the microwave resonators enables to create quantum phonon states, manipulate hybrid entanglement between phonons and photons and generate 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.

5 pages, 4 figures