Improved "Position Squared" Readout of a Mechanical Resonator in an Optical Cavity Using Degenerate Optical Modes

TL;DR

This paper enhances the sensitivity of position squared ($x^2$) measurements in optomechanical systems by using nearly degenerate optical modes, enabling better quantum state detection of a mechanical resonator.

Contribution

It introduces a method to significantly improve $x^2$ readout sensitivity by employing nearly degenerate transverse cavity modes and provides a theoretical framework for tunable $x^2$-coupling.

Findings

Achieved orders of magnitude improvement in $x^2$ sensitivity.

Derived a perturbation theory matching experimental results.

Theoretically demonstrated tunability of $x^2$-coupling.

Abstract

Optomechanical devices in which a flexible SiN membrane is placed inside an optical cavity allow for very high finesse and mechanical quality factor in a single device. They also provide fundamentally new functionality: the cavity detuning can be a quadratic function of membrane position. This enables a measurement of "position squared" ($x^2$) and in principle a QND phonon number readout of the membrane. However, the readout achieved using a single transverse cavity mode is not sensitive enough to observe quantum jumps between phonon Fock states. Here we demonstrate an $x^2$-sensitivity that is orders of magnitude stronger using two transverse cavity modes that are nearly degenerate. We derive a first-order perturbation theory to describe the interactions between nearly-degenerate cavity modes and achieve good agreement with our measurements using realistic parameters. We also demonstrate theoretically that the $x^2$-coupling should be easily tunable over a wide range.