Driving a mechanical resonator in to coherent states via random measurements

We propose dynamical schemes to engineer coherent states of a mechanical resonator coupled to an ancillary, superconducting flux qubit. The flux qubit, when repeatedly projected on to its ground state drives the mechanical resonator in to a coherent state in probabilistic, albeit heralded fashion. Assuming no operations on the state of the mechanical resonator during the protocol, coherent states are successfully generated only up to a certain value of the displacement parameter. This restriction can be overcome at the cost of a one-time operation on the initial state of the mechanical resonator. We discuss the possibility of experimental realization of the presented schemes.