Quantum State Reconstruction of an Oscillator Network in an Optomechanical Setting

TL;DR

This paper presents a method for reconstructing the quantum state of a mechanical oscillator network using optomechanical interactions and cavity measurements, with a focus on Gaussian states and potential extensions to single-photon regimes.

Contribution

It introduces a novel scheme for quantum state reconstruction in oscillator networks via controlled optomechanical interactions and cavity measurements.

Findings

Effective reconstruction of Gaussian states demonstrated numerically.

The scheme encodes quadrature statistics into cavity fields for measurement.

Potential pathways for extending to single-photon optomechanics discussed.

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.