Quantum description of radiative decay in optical cavities

Abstract

We present, for the first time, the quantum mechanical description of light-matter interaction in the presence of optical cavities that are characterized by radiative losses. Unique to radiative losses is the unitary evolution and their full preservation of the coherence, in stark contrast to the usually considered dissipative losses. We elucidate the reduction of exact quantum electrodynamic equations to a form similar to the familiar Jaynes-Cummings model through the introduction and study of a new class of noise operators. The dynamics of this henceforth inherently dissipative model are then presented by formulating the resulting equations of motion. Furthermore, an input- output formalism is established, which provides a direct connection to the dynamics of output states accessible with detectors. The application-oriented cases of coherent and pulsed laser pumping are discussed as inputs. Finally the single-photon dynamics in an optical cavity with significant radiative loss - whose importance has to be contextualized in view of the prospects of light-matter interaction applications - are reviewed according to the proposed model. The formulation is kept as general as possible to emphasise the universal applicability to different implementations of quantum optical systems but from our own background we have an application in mind in the context of nanooptics.