Spontaneous transition rates near the focus of a parabolic mirror with identification of the vectorial modes involved

TL;DR

This paper calculates spontaneous emission rates near a parabolic mirror's focus, revealing how specific vectorial modes can enhance atomic transitions and enable quantum control in localized regions.

Contribution

It provides a detailed analysis of electromagnetic modes in a parabolic mirror and their impact on atomic spontaneous emission, highlighting mode-specific enhancement effects.

Findings

Electric dipole transitions are enhanced near the mirror focus.

The relevant vectorial modes can be clearly identified.

Enhancement effects diminish away from the focus, but few modes remain relevant.

Abstract

Each natural mode of the electromagnetic field within a parabolic mirror exhibits spatial localization and polarization properties that can be exploited for the quantum control of its interaction with atomic systems. The region of localization is not restricted to the focus of the mirror leading to a selective response of atomic systems trapped on its vicinity. We report calculations of the spontaneous emission rates for an atom trapped inside the mirror accounting for all atomic polarizations and diverse trapping regions. It is shown that electric dipole transitions can be enhanced near the focus of a deep parabolic mirror with a clear identification of the few vectorial modes involved. Out of the focus the enhancement vanishes gradually, but the number of relevant modes remains small. Ultimately this represents a quantum electrodynamic system where internal and external degrees of freedom cooperate to maximize a selective exchange and detection of single excitations.