Spontaneous Photon Emission in Cavities

TL;DR

This paper analyzes spontaneous photon emission from two-level atoms in parabolic and ellipsoidal cavities, using semiclassical methods to calculate excitation probabilities and energy densities, and compares these with numerical results.

Contribution

It develops photon path representations for transition amplitudes in multimode cavities, valid in the optical regime, bridging semiclassical and numerical approaches.

Findings

Semiclassical results match numerical simulations well.

Photon emission probabilities are accurately described even when wavelength exceeds cavity scales.

Diffraction effects are significant in the dynamical regime, challenging geometric optics.

Abstract

We investigate spontaneous photon emission processes of two-level atoms in parabolic and ellipsoidal cavities thereby taking into account the full multimode scenario. In particular, we calculate the excitation probabilities of the atoms and the energy density of the resulting few-photon electromagnetic radiation field by using semiclassical methods for the description of the multimode scenario. Based on this approach photon path representations are developed for relevant transition probability amplitudes which are valid in the optical frequency regime where the dipole and the rotating-wave approximations apply. Comparisons with numerical results demonstrate the quality of these semiclassical results even in cases in which the wave length of a spontaneously emitted photon becomes comparable or even larger than characteristic length scales of the cavity. This is the dynamical regime in which diffraction effects become important so that geometric optical considerations are typically not applicable.