Abstract
We study the dynamics of photon-hopping conduction between impurity atoms in a photonic band gap via resonance dipole-dipole interaction (RDDI) in the low-excitation density limit. This is done both in the absence and in the presence of a localized dielectric defect mode. The random impurity atom positions are modeled by means of a Gaussian random distribution of RDDI's with variance J and atomic line fluctuations with variance \ensuremath{\delta}. By numerical calculation, we demonstrate the occurrence of a number of collective quantum features of photon-hopping conduction. These include collective enhancement of the energy-transfer rate and collectively induced transparency within the dielectric cavity mode. These effects are shown to depend sensitively on the variances J and \ensuremath{\delta}. Our results suggest that RDDI mediated hopping conduction may protect atomic excitation energy from dissipation through nonradiative relaxation channels.
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