Tomography of an Optomechanical Oscillator

Optomechanical systems provide an attractive testbed for the creation and manipulation of nonclassical states of mechanical motion. A key experimental challenge is demonstrating that the desired quantum state has actually been prepared. We propose a new, realistic, experimental protocol for quantum state tomography of nonclassical states in optomechanical systems. Using a parametric drive, the procedure overcomes the challenges of weak optomechanical coupling and thermal noise to provide high efficiency homodyne measurement. Our analysis is based on the theoretical description of the generalised measurement that is performed when optomechanical position measurement competes with thermal noise and the parametric drive. The proposed experimental procedure is numerically simulated in realistic parameter regimes, which allows us to show that tomographic reconstruction of otherwise unverifiable nonclassical states is made possible.