In this chapter we aim at bringing together the fields of quantum control theory and quantum optomechanics, exploring the prospects of entanglement-enhanced quantum control of these systems. We first analyze in detail how the radiation pressure interaction can be used to generate entanglement between a mechanical mode and the electromagnetic field, both in continuous-wave and pulsed regimes, and introduce an optomechanical teleportation scheme to transfer an arbitrary quantum state from a traveling-wave light pulse onto the mechanical system. Making use of continuous measurement and optimal control theory, we then show how similar schemes can be implemented in a time-continuous regime; analyzed protocols include optimal optomechanical feedback cooling, time-continuous teleportation, and time-continuous entanglement swapping. Finally we discuss the implementation of a Kalman filter for an optomechanical system, representing an important first step toward the experimental realization of the discussed protocols. Additionally, elementary aspects of quantum stochastic calculus and quantum control theory are given in comprehensive appendices.
Publication:
Quantum Control of Optomechanical Systems; S.G. Hofer, K. Hammererin: Advances; In: Atomic, Molecular, and Optical Physics, Volume 66, 2017, Pages 263-374
