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.Comment: 19 pages, 3 figure