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We propose a protocol for quantum state tomography of nonclassical states inoptomechanical systems. Using a parametric drive, the procedure overcomes thechallenges of weak optomechanical coupling, poor detection efficiency, andthermal noise to enable high efficiency homodyne measurement. Our analysis isbased on the analytic description of the generalized measurement that isperformed when optomechanical position measurement competes with thermal noiseand a parametric drive. The proposed experimental procedure is numericallysimulated in realistic parameter regimes, which allows us to show thattomographic reconstruction of otherwise unverifiable nonclassical states ismade possible.

Tomography of an optomechanical oscillator via parametrically amplified position measurement