Enviat per Angelina Navarro el

Abstract

Modeling electromagnetic field-matter interaction plays an essential role in technology and

science. Solving classical Maxwell’s equations with bulk electromagnetic parameters

including permittivity and permeability is a commonly-used tool to understand physical

effects and optimize engineering designs. At the quantum regime, when the size of

quantum particles (atoms, molecules, quantum dots, and superconducting circuits) is

pretty small compared to wavelength (typically smaller than 10 nm at optical frequencies),

the “homogenized” bulk permittivity and permeability of the classical Maxwell equation is

invalid or meaningless to describe electromagnetic responses of the quantum particles. In

this situation, quantum effects become significant and therefore the particle system needs

to be quantized.

If the field intensity is strong or the number of photons is large, semi-classical Maxwell-

Schrödinger system is adopted to simulate the electromagnetic field-particle interaction,

where electromagnetic field is treated as a classical field interacting with the quantum

particles. The coupled Maxwell-Schrödinger system can be solved by a unified

Hamiltonian approach with a symplectic framework. Versatile interesting physical

phenomena involving Rabi-oscillation, radiative decay and shift, electromagnetically

induced transparency, saturable absorption, and high-harmonic generation can be

reproduced by the semi-classical framework.

If the field intensity is very weak or the number of photons is quite small, both particle

system and electromagnetic system must be quantized and classical Maxwell equation

breaks down. Regarding quantization of Maxwell equation in lossy and dispersive media,

the quantized field-matter-bath system is still an energy-conserving Hamiltonian system.

When the matter couples to a heat bath (environment), it loses energy to the bath;

simultaneously, the bath feeds the energy back to the matter system. This obeys the spirits

of thermal equilibrium, fluctuation-dissipation theorem, and detailed balance theory. As a

result, we could introduce the loss to the quantized field-matter system by regarding the

heat bath as a Langevin source or noise current. The use of ubiquitous Green’s function is

still present in the full quantum calculations, which find rich applications in a great amount

of cutting-edge problems, such as spontaneous emission, single photon detection, cavity

quantum electrodynamics, and quantum interference.