Quantum State Reconstruction of an Oscillator Network in an Optomechanical Setting

Abstract

We introduce a scheme to reconstruct an arbitrary quantum state of a mechanical oscillator network. We assume that a single element of the network is coupled to a cavity field via a linearized optomechanical interaction, whose time dependence is controlled by a classical driving field. By designing a suitable interaction profile, we show how the statistics of an arbitrary mechanical quadrature can be encoded in the cavity field, which can then be measured. We discuss the important special case of Gaussian state reconstruction, and study numerically the effectiveness of our scheme for a finite number of measurements. Finally, we speculate on possible routes to extend our ideas to the regime of single-photon optomechanics.

11 pages, 6 figures; v2: appendix added, minor modifications, close to published version

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• Quantum Communication Between Remote Mechanical Resonators
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• Unified framework to determine Gaussian states in continuous variable systems
• Arbitrary multimode Gaussian operations on mechanical cluster states
• Simultaneous retrodiction of multi-mode optomechanical systems using matched filters
• Generation of stable Gaussian cluster states in optomechanical systems with multifrequency drives