A theoretical framework for the Hamiltonian of angular momentum optomechanical system

TL;DR

This paper introduces a theoretical framework to derive Hamiltonians for angular momentum optomechanical systems, expanding the understanding of optical torques and angular momentum exchange in quantum optomechanics.

Contribution

It presents a novel theoretical approach for Hamiltonian derivation in angular momentum optomechanics, including complex systems with non-unit reflection coefficients.

Findings

Derived Hamiltonians for orbital and spin angular momentum systems

Extended framework to complex systems with multiple torsional oscillators

Demonstrated general applicability of the theoretical approach

Abstract

Photon carries linear momentum and angular momentum simultaneously. Within the light-matter interaction process, exchange of linear momentum results in optical forces, whereas exchange of angular momentum leads to optical torques. Use of optical forces (light pressure or damping) have been long and wide in quantum optomechanics, however, those of optical torque and optical angular momentum are not. Here we propose a theoretical framework based on optical angular momentum and optical torques to derive the Hamiltonians of cavity orbital and spin angular momentum optomechanical systems, respectively. Moreover, based on the method, we successfully obtain the Hamiltonian of the complex angular momentum optomechanical systems consisting of micro-cavity and several torsional oscillators, whose reflection coefficients are non-unit. Our results indicate the general applicability of our theoretical framework for the Hamiltonian of angular momentum optomechanical systems and extend the research scope of quantum optomechanics.