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Physical Review A

Electrostatic model of coherent decay in a small spherical sample of two-level atoms of radially varying density

Richard M. Friedberg, Jamal T. Manassah

Published Mar 28, 2012• 4 citations
Publisher

Abstract

We show that the decay rate and the frequency shift of the radiation modes from a small sphere of two-level atoms with varying radial density can be accurately obtained using an electrostatic model.Received 28 September 2011DOI:https://doi.org/10.1103/PhysRevA.85.033834©2012 American Physical Society

DOI
10.1103/physreva.85.033834

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We show that the decay rate and the frequency shift of the radiation modes from a small sphere of two-level atoms with varying radial density can be accurately obtained using an electrostatic model.Received 28 September 2011DOI:https://doi.org/10.1103/PhysRevA.85.033834©2012 American Physical Society
It is a familiar fact that, in an isolated sphere or ellipsoid of uniform polarization density, the electrostatic field also is uniform. Because of this, the state of uniform polarization in a spherical sample of uniformly distributed two-level atoms is an eigenmode of the coherent decay process in the limit of a small radius compared to the resonant wavelength of a single atom. Consequently, in this special geometry, the Dicke picture of uniform exponential decay should hold. In nonspheroidal geometries or in spherical geometries with nonuniform atomic density, the decay should be more complicated. Here, we find the characteristic equations that determine the eigenmodes of the Lienard-Wiechert interaction for a partly hollowed sphere of identical two-level atoms in two different radial configurations. We show that the Dicke picture for emission from a coherently prepared sample does not correctly describe the system's dynamics even when we take the radius of the sphere to be much smaller than the radiation wavelength.
We present a general formalism for studying the cavity quantum electrodynamics for an atom or a radiating dipole inside a hollow spherical cavity. The atomic-energy-level shifts and the modified dipolar decay rates are calculated in specific cases. In particular, the energy shifts for an atom located at the center of an empty sphere (radius a) vary as 1/a4{\mathit{a}}^{4}a4 for large ka and 1/a2{\mathit{a}}^{2}a2 for small ka, where k is the wave number. We attribute these variations to the retarded Casimir-Polder interaction and the state-independent vacuum-field contribution, respectively. \textcopyright{} 1996 The American Physical Society.