Two-mode back-action-evading measurements in cavity optomechanics

TL;DR

This paper proposes a three-mode optomechanical scheme enabling back-action-evading measurements of collective mechanical quadratures, allowing quantum-limited force measurement and steady-state entanglement generation between mechanical oscillators.

Contribution

It introduces a two-tone driving method for cavity optomechanics to perform back-action-evading measurements and generate mechanical entanglement, advancing quantum measurement and control techniques.

Findings

Enables measurement of mechanical quadratures beyond the quantum limit.

Demonstrates generation of steady-state mechanical entanglement.

Analyzes effects of dissipation and imperfections on measurement and entanglement.

Abstract

We study theoretically a three-mode optomechanical system where two mechanical oscillators are coupled to a single cavity mode. By using two-tone (i.e. amplitude-modulated) driving of the cavity, it is possible to couple the cavity to a single collective quadrature of the mechanical oscillators. In such a way, a back-action-evading measurement of the collective mechanical quadrature is possible. We discuss how this can allow one to measure both quadratures of a mechanical force beyond the full quantum limit, paying close attention to the role of dissipation and experimental imperfections. We also describe how this scheme allows one to generate steady-state mechanical entanglement; namely, one can conditionally prepare an entangled, two-mode squeezed mechanical state. This entanglement can be verified directly from the measurement record by applying a generalized version of Duan's inequality; we also discuss how feedback can be used to produce unconditional entanglement.