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.
Highlights
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 theory of spontaneous emission is centered on the idea that an emitter interacts with the surrounding electromagnetic (EM) environment, constantly probing its spatial and spectral structure
The emission rate can be manipulated by restricting the spectral mode density inside the cavity, but, due to the apertures required to control the electronic motion, the electron still interacts with a large number of spatial modes
Summary
Vectorial parabolic m odes[19] define the natural basis to describe the EM field inside a parabolic mirror. We have adopted the circular polarization basis {eσ } = {e± = ex ± iey, e0 = ez} to highlight the coupling between σ and m into an effective winding number n = m − σ for each component of the potential π (γ ). This structure is inherited to f (γ ). All parabolic vectorial γ-modes exhibit a high degree of spatial localization, displaying narrow regions of maximum intensity near a plane defined by a particular value Z of the z-coordinate. Such that the maximum amplitude is achieved near the plane Z ∼ −2κc/ω.
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