Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Journal of Nanchang University

RESONANCE DIPOLE-DIPOLE INTERACTION AND PHOTON-HOPPING CONDUCTION IN PHOTONIC CRYSTALS

Wei Xie

Published Jan 1, 2001• 0 citations
OpenAlex

Abstract

The density matrix theroy is used to study photon-hopping via resonance dipole-dipole interaction in photonic crystals.The condition of hopping is discussed.It is shown that when the most of atoms are in the unexcited states,the energy can not transmit from the excited atoms to the unexcited atoms without defect mode.The energy-transfer rate from the defect mode to the atoms is dependent on the ration of the RDDI coefficient to the atom-photon coupling coefficient.

Related papers

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

Sajeev John, Tran Quang

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.

Physical Review A•Nov 1, 1995•64 citations

Two-atom resonant radiative coupling in photonic band structures

Gershon Kurizki

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.

Physical Review A•Sep 1, 1990•110 citations

Resonant dipole-dipole interaction in a cavity

Takayoshi Kobayashi, Qianbing Zheng, Takashi Sekiguchi

Resonant dipole-dipole interaction (RDDI) in a Fabry-P\'erot cavity is studied by the mode-expansion method. It is shown that the RDDI depends upon three factors: the length of the cavity, the positions of molecules, and the polarization of dipoles. It is also revealed by the mode-expansion calculation that, instead of contributions only from the propagating modes, the RDDI can also be assisted by the evanescent photons in the cavity. The expressions of energy transfer rate are obtained both for the two-level model and multilevel one in terms of observed spectral shape functions.

Physical Review A•Oct 1, 1995•85 citations

Microcavity-induced modification of the dipole-dipole interaction

G. S. Agarwal, S. Dutta Gupta

We consider the feasibility of controlling the energy transfer between an unexcited and an excited atom using microcavities. The excitation-transfer probability is related to the strength of the dipole-dipole interaction and thus the excitation-transfer rates could be increased by enhancing the dipole-dipole interaction. We demonstrate this enhancement with an explicit three-dimensional calculation for a metallic cavity, which we characterize with a realistic dielectric function. We also demonstrate the shifts in cavity resonances from their ideal positions $m\ensuremath{\lambda}/2$ ($m$ is an integer and \ensuremath{\lambda} is the wavelength).

Physical Review A•Jan 1, 1998•94 citations

Atom-atom interaction in strongly modified reservoirs

Søren Bay, P. Lambropoulos, Klaus Mølmer

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.

Physical Review A•Feb 1, 1997•118 citations

Numerical simulations of photon trapping in doped photonic crystals doped with multi‐level atoms

Mahi R. Singh, I. Haque

A theory of photon trapping has been developed in photonic band-gap (PBG) and dispersive polaritonic band-gap (DPBG) materials doped with an ensemble of five-level atoms. These materials have gaps in their photon energy spectra. The atoms are prepared as coherent superpositions of the two lower states and interact with a reservoir and two photon fields. They also interact with each other by dipole-dipole interaction. The Schrödinger equation and the Laplace transform method are used to calculate the expressions for the number densities of the atomic states. Numerical simulations for a PBG material reveal that when the resonance energies lie away from the band edges and within the lower or upper bands, trapping is observed at certain values of the relative Rabi frequency associated with the two fields, which vary depending on the strength of the dipole-dipole interaction between the atoms. Also, if the photon fields are held constant, the population densities of the excited states of the atoms increase with increasing dipole-dipole interaction. These are very interesting phenomena. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Physica status solidi. C, Conferences and critical reviews/Physica status solidi. C, Current topics in solid state physics•May 1, 2005•7 citations
The density matrix theroy is used to study photon-hopping via resonance dipole-dipole interaction in photonic crystals.The condition of hopping is discussed.It is shown that when the most of atoms are in the unexcited states,the energy can not transmit from the excited atoms to the unexcited atoms without defect mode.The energy-transfer rate from the defect mode to the atoms is dependent on the ration of the RDDI coefficient to the atom-photon coupling coefficient.
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.
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.
Resonant dipole-dipole interaction (RDDI) in a Fabry-P\'erot cavity is studied by the mode-expansion method. It is shown that the RDDI depends upon three factors: the length of the cavity, the positions of molecules, and the polarization of dipoles. It is also revealed by the mode-expansion calculation that, instead of contributions only from the propagating modes, the RDDI can also be assisted by the evanescent photons in the cavity. The expressions of energy transfer rate are obtained both for the two-level model and multilevel one in terms of observed spectral shape functions.
We consider the feasibility of controlling the energy transfer between an unexcited and an excited atom using microcavities. The excitation-transfer probability is related to the strength of the dipole-dipole interaction and thus the excitation-transfer rates could be increased by enhancing the dipole-dipole interaction. We demonstrate this enhancement with an explicit three-dimensional calculation for a metallic cavity, which we characterize with a realistic dielectric function. We also demonstrate the shifts in cavity resonances from their ideal positions $m\ensuremath{\lambda}/2$ (mmm is an integer and \ensuremath{\lambda} is the wavelength).
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.
A theory of photon trapping has been developed in photonic band-gap (PBG) and dispersive polaritonic band-gap (DPBG) materials doped with an ensemble of five-level atoms. These materials have gaps in their photon energy spectra. The atoms are prepared as coherent superpositions of the two lower states and interact with a reservoir and two photon fields. They also interact with each other by dipole-dipole interaction. The Schrödinger equation and the Laplace transform method are used to calculate the expressions for the number densities of the atomic states. Numerical simulations for a PBG material reveal that when the resonance energies lie away from the band edges and within the lower or upper bands, trapping is observed at certain values of the relative Rabi frequency associated with the two fields, which vary depending on the strength of the dipole-dipole interaction between the atoms. Also, if the photon fields are held constant, the population densities of the excited states of the atoms increase with increasing dipole-dipole interaction. These are very interesting phenomena. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)