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arXiv:quant-ph/9905069 · Physical Review A

Spontaneous emission between two parallel plates, one or both infinitely permeable

Danilo T. Alves, Carlos Farina, Alexandre Carlos Tort

Published Feb 11, 2000• 39 citations
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Abstract

We compute the influence on the spontaneous-emission rate for a two-level atom when it is located between two parallel plates of a different nature, namely a perfectly conducting plate $(\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\epsilon}}\ensuremath{\infty})$ and an infinitely permeable one $(\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\mu}}\ensuremath{\infty}).$ We also discuss the case of two infinitely permeable plates. We compare our results with those found in the literature for the case of two perfectly conducting plates.

DOI
10.1103/physreva.61.034102

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We compute the influence on the spontaneous-emission rate for a two-level atom when it is located between two parallel plates of a different nature, namely a perfectly conducting plate (\ensuremathϵ\ensuremath→\ensuremath∞)(\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\epsilon}}\ensuremath{\infty})(\ensuremathϵ\ensuremath→​\ensuremath∞) and an infinitely permeable one (\ensuremathμ\ensuremath→\ensuremath∞).(\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\mu}}\ensuremath{\infty}).(\ensuremathμ\ensuremath→​\ensuremath∞). We also discuss the case of two infinitely permeable plates. We compare our results with those found in the literature for the case of two perfectly conducting plates.
We investigate the generation of quantum interference induced by spontaneous emission from two transitions of a V-type three-level atom embedded between two parallel plates (one or both the plates have infinite permeability, i.e. μ→ ∞ ). The result shows that, due to the anisotropy of vacuum, quantum interference still exists although the two dipole matrix elements of the atom are orthogonal to each other. When the atom is located very close to one of the plates, the quantum interference effect is particularly prominent. The strength of quantum interference displays oscillating behaviour with the position of the atom. With the increase of the distance between the plates, the oscillation becomes dense.
The spontaneous emission rate $\ensuremath{\gamma}$ of a two-level atom inside a chaotic cavity fluctuates strongly from one point to another because of fluctuations in the local density of modes. For a cavity with perfectly conducting walls and an opening containing NNN wave channels, the distribution of $\ensuremath{\gamma}$ is given by $P(\ensuremath{\gamma})\ensuremath{\propto}{\ensuremath{\gamma}}^{N/2\ensuremath{-}1}(\ensuremath{\gamma}+{\ensuremath{\gamma}}_{0}{)}^{\ensuremath{-}N\ensuremath{-}1}$, where ${\ensuremath{\gamma}}_{0}$ is the free-space rate. For small NNN the most probable value of $\ensuremath{\gamma}$ is much smaller than the mean value ${\ensuremath{\gamma}}_{0}$.
We study the spontaneous-emission of a single atom located between two parallel infinite plates where one of the plates is partially reflective and the plate separation is of the order of the wavelength of the atomic transition. We pay particular attention to the nature of the field modes in such a finite finesse cavity, including the full three-dimensional nature of the field. We then compute the decay rate of an excited atom placed inside such a cavity. The angular distributions of the spontaneous-emission and of the cavity field vacuum fluctuation variances are investigated. Finally, we examine the output field from an atom inside a finite finesse microcavity. We show that the radiation transmitted outside such microcavity forms a nondiffracting Bessel beam. \textcopyright{} 1996 The American Physical Society.
The rate of spontaneous emission of an atom in the presence of an interface between two dielectrics was calculated using the quantum theory of electromagnetic radiation. Spatial distribution of the field for quasi-continuous spectrum inside an infinite cavity with ideally conducting walls was determined for multiple values of real refractive indices. Spontaneous emission in the continuous spectrum of the field was calculated using the known spatial Green’s function for a one-dimensional dielectric interface. The rate of spontaneous emission of an atom may either be higher or much lower than that in the free space, depending on the refractive indices and the distance between the atom and the interface between dielectrics.
It is a well known fact that the presence of material bodies in the vicinity of an atom affects its interaction with the always present quantized electromagnetic field. In this paper, we focus on how the spontaneous-emission rate of a given excited atom is altered when this atom is placed inside a perfectly conducting wedge. We begin by briefly presenting the formalism upon which our calculations are founded, proceeding then to a long but straightforward calculation of the transition rate. We present results for a general atom, but, for the sake of simplicity, we narrow them down to an effective two-level system in our numerical investigations. The oscillatory pattern for the spontaneous-emission rate of the atom as we vary its relative position to the wedge as well as the phenomenon of suppression are shown by a few graphs.
The interaction between electromagnetic radiation and two two-level atoms with different resonance frequencies near a perfectly conducting metal surface is considered. The atom-atom and atom-surface separations are assumed to be smaller than the corresponding mean resonance wavelength. A quantum-mechanical version of the image method is adopted to study the spontaneous emission by such an atomic pair. Within the framework of this approach, each individual atom and its corresponding image are kinematically correlated, while dynamically they are in effect independent. The total radiation rate of the atomic system is calculated as a function of time for various values of frequency difference. Explicit results are given for several different initial states of the atomic system. Some of them exhibit superradiance, and some initially act as photon-trapping states and eventually are able to undergo radiative decay. Oscillations as a manifestation of beating appear in the time evolution of the radiation rate in all cases of the various initial states, when the frequency difference becomes larger than a critical value given as twice the mean halfwidth of the atomic resonance lines.