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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 measureand manipulate the phonon state due to the tiny motion in the quantum regime.On the other hand, microwave resonators are powerful quantum devices sincearbitrary photon state can be synthesized and measured with a quantumtomography. We show that a linear coupling, strong and controlled with a gatevoltage, between the mechanical and the microwave resonators enables to createquantum phonon states, manipulate hybrid entanglement between phonons andphotons and generate entanglement between two mechanical oscillators. Incircuit quantum optomechanics, the mechanical resonator acts as a quantumtransducer between an auxiliary quantum system and the microwave resonator,which is used as a quantum bus.

Quantum transducer in circuit optomechanics