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Physical Review A

Photon-hopping conduction and collectively induced transparency in a photonic band gap

Sajeev John, Tran Quang

Published Nov 1, 1995• 64 citations
Publisher

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.

DOI
10.1103/physreva.52.4083

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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.
We describe the collective optical properties of impurity two-level atoms in a photonic band gap interacting by resonance dipole-dipole interaction (RDDI) and coupled to a localized cavity mode. The random impurity atom positions are modeled by means of a Gaussian random distribution of RDDI's with variance JJJ and atomic line fluctuation with variance $\ensuremath{\delta}$. We demonstrate the occurrence of a new collective atomic steady state, the optical analog of a spin-1/2 dipolar glass, and an associated Bose-glass state of photons in the cavity mode.
We discuss the nonlinear response of impurity two-level atoms in a pseudophotonic band gap (PBG) to an applied laser field. It is shown that in the case when the variance of resonant dipole-dipole interaction (RDDI) is much larger than its average value and the spontaneous emission rate, a nonequilibrium second-order phase transition occurs when the applied field strength parameter exceeds the variance of RDDI. This situation arises when the atomic density is low and the resonance frequency is near the center of a wide PBG. At this threshold the system changes from glassy phase to ferroelectric phase. In the case when the average value of RDDI is larger than its variance and spontaneous emission decay rate, this phase transition becomes first order, leading to optical bistability. This situation arises when the atomic density is high or when the photon localization length within the PBG extends over many optical wavelengths. The influence of RDDI fluctuation on bistability is discussed. These results suggest that disordered, impurity-doped, PBG materials may exhibit very low threshold switching properties. \textcopyright{} 1996 The American Physical Society.
Radiative coupling between identical atoms sharing an excitation is studied in media where dispersion creates photonic band gaps, i.e., forbidden bands of light propagation for all directions and polarizations. Photonic band gaps can exist in media whose dielectric index exhibits strong three-dimensionally periodic modulations (``photonic crystals'') or in bands of polaritonic media. It is shown that the resonant dipole-dipole interaction as well as cooperative fluorescence of two-atom systems can be strongly enhanced or suppressed, to the extent of being essentially eliminated, by one of the following mechanisms: (a) dependence on location of the atoms within a unit cell of a photonic crystal, i.e., sensitivity to the spatial variation of the field normal modes; (b) dependence on the density of normal modes in allowed bands and on the density of virtual (evanescent) modes in band gaps. The ability to suppress the dipole-dipole interactions at interatomic separations characterizing quasimolecules would have far-reaching implications on their dissociative or collisional dynamics, spectroscopy, and rates of energy transfer.
We study the dielectric response of impurity two-level atoms in a photonic band gap (PBG) to an applied laser field. In this system, the atoms may exchange energy coherently by resonance dipole-dipole interaction (RDDI) which is assumed to be strong compared to the spontaneous emission rate. When the applied Rabi frequency exceeds the RDDI energy scale, nonlinear saturation of the absorptive part of the susceptibility occurs while the real part of the nonlinear susceptibility remains large. This suggests that doped PBG materials may act as nearly lossless, but highly nonlinear dielectrics.
We extend recent work on two closely spaced atoms interacting through the narrow band of strongly coupled modes at the edge of a photonic band gap. The resonant dipole-dipole interaction (RDDI) is strongly modified for atomic transition frequencies in the vicinity of the band-gap edge, but we show that an analytical approximation to the RDDI agrees very well with the exact RDDI obtained by numerical integration using the exact dispersion relation. Having established the value of the RDDI, we can derive the amplitudes for the two atoms without resorting to the pole approximation which is necessary due to the strongly modified mode structure in the dielectric host. For a wide range of parameters we find beating and population trapping in the long time limit. The distribution of population in the photonic continuum is investigated in the long time limit in the case of one and two atoms. It is found to be strongly asymmetric and to exhibit a strong signature of the unusual mode structure in the material at the band-gap edge.