On the Interaction of Massive Photons and Mechanical Oscillators in Cavity Optomechanics: Basic Model and Quantization

Abstract

This study investigates the theoretical aspects of the interaction between photons with mass and a mechanical oscillator as drawn within the framework of cavity optomechanics. The study employs Proca theory as the mathematical framework to initially describe the dynamics of massive photons in a Fabry‐Perot cavity with a movable mass, both in classical and quantum scenarios. It quantifies the modifications induced by the nonzero photon mass, considering first‐ and second‐order effects, and derives expressions for the amplification of radiation pressure resulting from the presence of nonzero photon mass. Additionally, it derives the Hamiltonian of the quantum optomechanical system, incorporating the effects of photon mass at first and second order. It anticipates that experimental realization of massive optomechanics can be achieved by utilizing Proca material, which is a spatio‐temporally dispersive material that exhibits behavior equivalent to Proca theory in a vacuum, thus enabling the study of the interaction between massive photons and mechanical systems in cavity‐based optomechanical setups (referred to as massive cavity optomechanics). The study presented here caters to a diverse audience with an interest in the analysis and measurement of interactions among massive objects at the quantum scale.