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

• Main Authors: Sankey, Jack C, Jayich, Andrew M, Zwickl, Benjamin M, Yang, Cheng, Harris, Jack G. E
• Format: Journal Article
• Language: English
• Published: 09.11.2008
• Subjects: Physics - Quantum Physics
• DOI: 10.48550/arxiv.0811.1343

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.