Quantum manipulation of a two-level mechanical system

We consider a nonlinearly coupled electromechanical system, and develop quantitative theory for two-phonon cooling. In the presence of cooling, mechanical Hilbert space is effectively reduced to its ground first excited states, allowing quantum operations at level individual phonons preparing nonclassical states with negative Wigner functions. propose scheme performing arbitrary Bloch sphere rotations, derive fidelity in specific case π-pulse. characterise detrimental processes that reduce coherence demonstrate our can be implemented state-of-the-art devices.