Corrections to the Optomechanical Hamiltonian from Quadratic Fluctuations of a Moving Mirror

TL;DR

This paper extends the optomechanical Hamiltonian to include quadratic fluctuations of a moving mirror, capturing higher-order effects crucial for strong coupling regimes in optomechanics and related fields.

Contribution

It introduces a generalized radiation pressure operator accounting for quadratic position fluctuations, advancing the theoretical understanding of mirror-field interactions.

Findings

Quadratic corrections to the Hamiltonian are significant in strong coupling regimes.

The generalized operator captures higher-order effects in mirror-field coupling.

Implications for optomechanics, electromechanics, and superconducting circuits.

Abstract

We extend the theory of the radiation pressure to include quadratic fluctuations in the position of a moving mirror. This enables the introduction of a generalized radiation pressure operator that captures higher-order effects in the mirror-field coupling. For mechanical resonators with frequencies comparable to the fundamental cavity frequency, the resulting corrections to the optomechanical Hamiltonian are quadratic in the standard radiation pressure coupling. These corrections are expected to play a significant role in the strong coupling regime of optomechanics, electromechanics, and superconducting circuit analogs.