  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.
