Dispersive optomechanics: a membrane inside a cavity

TL;DR

This paper combines theoretical and experimental analysis of dispersively coupled membrane-in-the-middle optomechanical systems, examining optical properties, laser cooling, and quantum non-demolition measurements with high precision.

Contribution

It provides detailed calculations and experimental validation of optical properties and quantum measurement techniques in membrane-in-the-middle optomechanics.

Findings

Excellent agreement between theory and experiment for high finesse cavities.

The imaginary part of the membrane's index of refraction is approximately 10^(-4).

Demonstrates potential for quantum non-demolition measurements of phonon number.

Abstract

We present the results of theoretical and experimental studies of dispersively coupled (or "membrane in the middle") optomechanical systems. We calculate the linear optical properties of a high finesse cavity containing a thin dielectric membrane. We focus on the cavity's transmission, reflection, and finesse as a function of the membrane's position along the cavity axis and as a function of its optical loss. We compare these calculations with measurements and find excellent agreement in cavities with empty-cavity finesses in the range 10^4 to 10^5. The imaginary part of the membrane's index of refraction is found to be approximately 10^(-4). We calculate the laser cooling performance of this system, with a particular focus on the less-intuitive regime in which photons "tunnel" through the membrane on a time scale comparable to the membrane's period of oscillation. Lastly, we present calculations of quantum non-demolition measurements of the membrane's phonon number in the low signal-to-noise regime where the phonon lifetime is comparable to the QND readout time.