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

TL;DR

This paper develops a quantum framework for electromagnetic scattering by a dielectric sphere, enabling analysis of quantum light interactions and correlations, with potential applications in quantum optics and nanophotonics.

Contribution

It introduces a quantization method for electromagnetic fields around a dielectric sphere and explores quantum scattering phenomena, including Hong-Ou-Mandel interference.

Findings

Derived analytical expressions for quantum scattering by spheres of arbitrary size.

Calculated the second-order correlation function revealing quantum interference effects.

Established a theoretical basis for quantum light interactions with dielectric particles.

Abstract

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.