Cavity Mode Frequencies and Strong Optomechanical Coupling in Two-Membrane Cavity Optomechanics

TL;DR

This paper analyzes the mode frequencies of a two-membrane cavity system, deriving analytical solutions that reveal the potential for achieving strong optomechanical coupling without significantly degrading cavity finesse.

Contribution

It provides approximate analytical formulas for cavity mode frequencies in a two-membrane system, demonstrating conditions for large optomechanical coupling in a simple cavity setup.

Findings

Large optomechanical coupling achievable with highly reflective membranes near inner cavity resonances

Cavity finesse remains high despite the presence of membranes under strong coupling conditions

The system can reach a regime where the coupling exceeds cavity decay rate, enabling strong coupling experiments

Abstract

We study the cavity mode frequencies of a Fabry-P\'erot cavity containing two vibrating dielectric membranes. We derive the equations for the mode resonances and provide approximate analytical solutions for them as a function of the membrane positions, which act as an excellent approximation when the relative and center-of-mass position of the two membranes are much smaller than the cavity length. With these analytical solutions, one finds that extremely large optomechanical coupling of the membrane relative motion can be achieved in the limit of highly reflective membranes when the two membranes are placed very close to a resonance of the inner cavity formed by them. We also study the cavity finesse of the system and verify that, under the conditions of large coupling, it is not appreciably affected by the presence of the two membranes. The achievable large values of the ratio between the optomechanical coupling and the cavity decay rate, $g/\kappa$, make this two-membrane system the simplest promising platform for implementing cavity optomechanics in the strong coupling regime.