Rotational optomechanical coupling of a spinning dielectric sphere

We formulate a non-relativistic Hamiltonian in order to describe how the rotational degrees of freedom of a dielectric sphere and quantized light fields are coupled. Such an interaction is shown to take a form of angular momentum coupling governed by the field angular momentum inside the dielectric. As a specific example, we show that the coupling due to a single whispering gallery mode can lead to precession dynamics and frequency shifts of light.