Quantum Electrodynamics with a Nonmoving Dielectric Sphere: Quantizing Lorenz-Mie Scattering

We quantize the electromagnetic field in the presence of a nonmoving dielectric sphere in vacuum. The sphere is assumed to be lossless, dispersionless, isotropic, and homogeneous. The quantization is performed using normalized eigenmodes as well as plane-wave modes. We specify two useful alternative bases of normalized eigenmodes: spherical eigenmodes and scattering eigenmodes. A canonical transformation between plane-wave modes and normalized eigenmodes is derived. This formalism is employed to study the scattering of a single photon, coherent squeezed light, and two-photon states off a dielectric sphere. In the latter case we calculate the second-order correlation function of the scattered field, thereby unveiling the angular distribution of the Hong-Ou-Mandel interference for a dielectric sphere acting as a three-dimensional beam splitter. Our results are analytically derived for an arbitrary size of the dielectric sphere with a particular emphasis on the small-particle limit. This work sets the theoretical foundation for describing the quantum interaction between light and the motional, rotational and vibrational degrees of freedom of a dielectric sphere.