Quantum Electrodynamics with a Nonmoving Dielectric Sphere: Quantizing Lorenz-Mie Scattering
arXiv:2106.07975 · doi:10.1364/JOSAB.498540
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.
arXiv comment19 pages, 3 figures
References in corpus (30)
- Motional Quantum Ground State of a Levitated Nanoparticle from Room Temperature
- Cavity optomechanics using an optically levitated nanosphere
- Millikelvin cooling of an optically trapped microsphere in vacuum
- Toward Quantum Superposition of Living Organisms
- Levitodynamics: Levitation and control of microscopic objects in vacuum
- Real-time optimal quantum control of mechanical motion at room temperature
- Quantum control of a nanoparticle optically levitated in cryogenic free space
- Optomechanics with Levitated Particles
- Optically Levitating Dielectrics in the Quantum Regime: Theory and Protocols
- Simultaneous ground-state cooling of two mechanical modes of a levitated nanoparticle
- Cavity cooling of an optically trapped nanoparticle
- Force and acceleration sensing with optically levitated nanogram masses at microkelvin temperatures
- Searching for new physics using optically levitated sensors
- Optimal Position Detection of a Dipolar Scatterer in a Focused Field
- Optical cold damping of neutral nanoparticles near the ground state in an optical lattice
- Theory for Cavity Cooling of Levitated Nanoparticles via Coherent Scattering: Master Equation Approach
- Two-dimensional quantum motion of a levitated nanosphere
- Quantum Model of Cooling and Force Sensing With an Optically Trapped Nanoparticle
- Master equation approach to optomechanics with arbitrary dielectrics
- Three-dimensional force-field microscopy with optically levitated microspheres
- Search for non-Newtonian interactions at micrometer scale with a levitated test mass
- Limits on the abundance of millicharged particles bound to matter
- Quantum displacement sensing and cooling in 3D levitated cavity optomechanics
- Coherent scattering 2D cooling in levitated cavity optomechanics
- All-optical sub-Kelvin sympathetic cooling of a levitated microsphere in vacuum
- High sensitivity, levitated microsphere apparatus for short-distance force measurements
- Levitated Optomechanics with Meta-Atoms
- Quantum theory of light interaction with a Lorenz-Mie particle: Optical detection and three-dimensional ground-state cooling
- Theory of nanoparticle cooling by elliptic coherent scattering
- Mode expansions in the quantum electrodynamics of photonic media with disorder