Non-adiabatic optomechanical Hamiltonian of a moving dielectric membrane in a cavity

TL;DR

This paper develops a non-adiabatic Hamiltonian for a moving dielectric membrane in a cavity, allowing multi-mode effects to be incorporated into quantum optomechanical models.

Contribution

It introduces a Hamiltonian formulation that does not rely on the single-mode adiabatic approximation, enabling more accurate modeling of multi-mode interactions.

Findings

Derived a non-relativistic Hamiltonian for membrane-cavity interaction

Constructed generalized Fock states for quantum description

Analyzed how photon scattering affects interaction strengths and membrane frequency

Abstract

We formulate a non-relativistic Hamiltonian in order to describe the interaction between a moving dielectric membrane and radiation pressure. Such a Hamiltonian is derived without making use of the single-mode adiabatic approximation, and hence it enables us to incorporate multi-mode effects in cavity optomechanics. By performing second quantization, we show how a set of generalized Fock states can be constructed to represent quantum states of the membrane and cavity field. In addition, we discuss examples showing how photon scattering among different cavity modes would modify the interaction strengths and the mechanical frequency of the membrane.