Position Estimation of a Parametrically Driven Optomechanical System

Abstract

We study the position estimation of a mechanical oscillator undergoing both detuned parametric amplification and continuous quantum measurement. This model, which can be utilised to produce squeezed states, is applied to a general optoelectromechanical system. Using a stochastic master equation formalism, we derive general formulae for the reduction in position uncertainty of one quadrature of motion. The filter for extracting the optimal position estimate from the measurement record is derived. We also find that since this scheme does not work far into the back-action dominated regime, implementing resolved-sideband cooling improves the squeezing only marginally.

16 pages, 5 figures

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• Quantum Langevin equations for optomechanical systems
• Classical non-Gaussian state preparation through squeezing in an opto-electromechanical resonator
• Mechanical Entanglement via Detuned Parametric Amplification
• Detuned Mechanical Parametric Amplification as a Quantum Non-Demolition Measurement
• Tomography of an optomechanical oscillator via parametrically amplified position measurement
• Squeezing of optomechanical modes in detuned Fabry-Perot interferometer