Quantum-state reconstruction of a mechanical mirror in a hybrid system

Abstract

We introduce a scheme to reconstruct the quantum state of a mechanical mirror in a hybrid optomechanical system. The scheme involves sending a beam of two-level atoms to interact with a quantized cavity field which is weakly coupled to the mechanical mirror. We show that the measured data of the excited-state probability of the atoms can be used directly to reconstruct the initial state of the mechanical mirror. If the mechanical mirror is initially a pure quantum state, we can reconstruct both the probability and the phase of the mechanical state. If it is initially a mixed state, we can reconstruct all the diagonal matrix elements and the first two diagonals above and below them.