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 the Optical Society of America B

Quantum electrodynamics in photonic band gaps: atomic-beam interaction with a defect mode

Gershon Kurizki, Boris Sherman, A. Kadyshevitch

Published Feb 1, 1993• 15 citations
Publisher

Abstract

A structural defect in a two-dimensionally periodic dielectric structure may form a local field mode within a photonic band gap in which no other E-polarized field modes exist. We show that such a defect mode can give rise to new quantum-electrodynamic effects in resonant field–atom interaction, owing to the spatially modulated standing-wave character of its field. Atomic-beam motion is considered (a) along an interplanar defect and (b) through a spherical defect. The resonant interaction of a moving two-level atom with the quantized field of these defects can yield hitherto unknown features—oscillatory patterns of the atomic population inversion, fluorescence spectra, and nonclassical field states—that are essentially different from their counterparts in the standard Jaynes–Cummings model, which holds for atomic-beam motion in a spatially uniform single-mode field.

DOI
10.1364/josab.10.000346

Related papers

Nonclassical field dynamics in photonic band structures: Atomic-beam resonant interaction with a spatially periodic field mode

Boris Sherman, Gershon Kurizki, A. Kadyshevitch

We consider the quantum electrodynamics of an atom uniformly moving through a single spatially periodic field mode. The shape and periodicity of the field modulation can be designed by an appropriate choice of a defect in a periodic structure that possesses a forbidden spectral band (a ``photonic band gap''). This design of the periodic modulation can improve our control over the evolution and properties (e.g., photon statistics) of nonclassical ``Schr\"odinger-cat'' states of the field, generated by resonant interaction with the atom.

Physical Review Letters•Sep 28, 1992•25 citations

Spontaneous and Induced Atomic Decay in Photonic Band Structures

Abraham G. Kofman, Gershon Kurizki, Boris Sherman

We present a comprehensive quantum electrodynamical analysis of the interaction between a continuum with photonic band gaps (PBGs) or frequency cut-off and an excited two-level atom, which can be either ‘bare’ or ‘dressed’ by coupling to a near-resonant field mode. A diversity of novel features in the atom and field dynamics is shown to arise from the non-Markovian character of radiative decay into such a continuum of modes. Firstly the excited atom is shown to evolve, by spontaneous decay, into a superposition of non-decaying single-photon dressed states, each having an energy in a different PBG, and a decaying component. This superposition is determined by the atomic resonance shift, induced by the spontaneously emitted photon, into or out of a PBG. The main novel feature exhibited by the decaying excited-state component is the occurrence of beats between the shifted atomic resonance frequency and the PBG cut-off frequencies, corresponding to a non-Lorentzian emission spectrum. Secondly the induced decay of a resonantly driven atom into such a continuum exhibits a cascade of transitions down the ladder of dressed states, which are labelled by decreasing photon numbers of the driving mode. Remarkably, this cascade is terminated at the dressed-state doublet, from which all subsequent transitions to lower doublets are forbidden because they fall within the PBG. This doublet then becomes an attractor state for the populations of higher-lying doublets. As a result, the photon-number distribution of the driving mode becomes strongly sub-Poissonian.

Journal of Modern Optics•Feb 1, 1994•324 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

Photonic band gaps and defect states induced by excitations of Bose-Einstein condensates in optical lattices

Karl-Peter Marzlin, Weiping Zhang

We study the interaction of a Bose-Einstein condensate in an optical lattice with an additional largely detuned light field propagating through it. If the condensate is in its ground state it acts as a periodic dielectric, and gives rise to photonic band gaps at optical frequencies. The band structure of the combined system of condensed lattice atoms and photons is studied by using the concept of polaritons. If elementary excitations of the condensate are present, they will produce defect states inside the photonic band gaps. The frequency of localized defect states is calculated using the Koster-Slater model.

arXiv:cond-mat/9810085•Physical Review A•Apr 1, 1999•23 citations

Quasimode theory of quantum optical processes in photonic band gap materials

Bryan J. Dalton, B. M. Garraway

This paper deals with atomic systems coupled to a structured reservoir of quantum EM field modes, with particular relevance to atoms interacting with the field in photonic band gap materials. The case of high Q cavities has been treated elsewhere using Fano diagonalization based on a quasimode approach, showing that the cavity quasimodes are responsible for pseudomodes introduced to treat non-Markovian behaviour. The paper considers a simple model of a photonic band gap case, where the spatially dependent permittivity consists of a constant term plus a small spatially periodic term that leads to a narrow band gap in the spectrum of mode frequencies. Most treatments of photonic band gap materials are based on the true modes, obtained numerically by solving the Helmholtz equation for the actual spatially periodic permittivity. Here the field modes are first treated in terms of a simpler quasimode approach, in which the quasimodes are plane waves associated with the constant permittivity term. Couplings between the quasimodes occur owing to the small periodic term in the permittivity, with selection rules for the coupled modes being related to the reciprocal lattice vectors. This produces a field Hamiltonian in quasimode form. A matrix diagonalization method may be applied to relate true mode annihilation operators to those for quasimodes. The atomic transitions are coupled to all the quasimodes, and the true mode atom-EM field coupling constants (one-photon Rabi frequencies) are related to those for the quasimodes and also expressions are obtained for the true mode density. The results for the one-photon Rabi frequencies differ from those assumed in other work. Expressions for atomic decay rates are obtained using the Fermi Golden rule, although these are valid only well away from the band gaps.

Journal of Modern Optics•Apr 1, 2002•3 citations

Dynamics of the Jaynes-Cummings model in the presence of photonic crystals

Ali A. Kamli, Smail B. Bougouffa

The three-level atom Jaynes-Cummings model is solved exactly and its dynamics investigated in photonic crystals that exhibit band gaps. The atom-field coupling and the probability amplitudes are evaluated as functions of the mode frequency and for different cavity parameters. Besides band-gap effects, the system exhibits novel local field effects. These show as peaks in the atom-field coupling and hence peaks or dips in the probability functions.

Journal of Modern Optics•Apr 1, 2002•1 citation
A structural defect in a two-dimensionally periodic dielectric structure may form a local field mode within a photonic band gap in which no other E-polarized field modes exist. We show that such a defect mode can give rise to new quantum-electrodynamic effects in resonant field–atom interaction, owing to the spatially modulated standing-wave character of its field. Atomic-beam motion is considered (a) along an interplanar defect and (b) through a spherical defect. The resonant interaction of a moving two-level atom with the quantized field of these defects can yield hitherto unknown features—oscillatory patterns of the atomic population inversion, fluorescence spectra, and nonclassical field states—that are essentially different from their counterparts in the standard Jaynes–Cummings model, which holds for atomic-beam motion in a spatially uniform single-mode field.
We consider the quantum electrodynamics of an atom uniformly moving through a single spatially periodic field mode. The shape and periodicity of the field modulation can be designed by an appropriate choice of a defect in a periodic structure that possesses a forbidden spectral band (a ``photonic band gap''). This design of the periodic modulation can improve our control over the evolution and properties (e.g., photon statistics) of nonclassical ``Schr\"odinger-cat'' states of the field, generated by resonant interaction with the atom.
We present a comprehensive quantum electrodynamical analysis of the interaction between a continuum with photonic band gaps (PBGs) or frequency cut-off and an excited two-level atom, which can be either ‘bare’ or ‘dressed’ by coupling to a near-resonant field mode. A diversity of novel features in the atom and field dynamics is shown to arise from the non-Markovian character of radiative decay into such a continuum of modes. Firstly the excited atom is shown to evolve, by spontaneous decay, into a superposition of non-decaying single-photon dressed states, each having an energy in a different PBG, and a decaying component. This superposition is determined by the atomic resonance shift, induced by the spontaneously emitted photon, into or out of a PBG. The main novel feature exhibited by the decaying excited-state component is the occurrence of beats between the shifted atomic resonance frequency and the PBG cut-off frequencies, corresponding to a non-Lorentzian emission spectrum. Secondly the induced decay of a resonantly driven atom into such a continuum exhibits a cascade of transitions down the ladder of dressed states, which are labelled by decreasing photon numbers of the driving mode. Remarkably, this cascade is terminated at the dressed-state doublet, from which all subsequent transitions to lower doublets are forbidden because they fall within the PBG. This doublet then becomes an attractor state for the populations of higher-lying doublets. As a result, the photon-number distribution of the driving mode becomes strongly sub-Poissonian.
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 interaction of a Bose-Einstein condensate in an optical lattice with an additional largely detuned light field propagating through it. If the condensate is in its ground state it acts as a periodic dielectric, and gives rise to photonic band gaps at optical frequencies. The band structure of the combined system of condensed lattice atoms and photons is studied by using the concept of polaritons. If elementary excitations of the condensate are present, they will produce defect states inside the photonic band gaps. The frequency of localized defect states is calculated using the Koster-Slater model.
This paper deals with atomic systems coupled to a structured reservoir of quantum EM field modes, with particular relevance to atoms interacting with the field in photonic band gap materials. The case of high Q cavities has been treated elsewhere using Fano diagonalization based on a quasimode approach, showing that the cavity quasimodes are responsible for pseudomodes introduced to treat non-Markovian behaviour. The paper considers a simple model of a photonic band gap case, where the spatially dependent permittivity consists of a constant term plus a small spatially periodic term that leads to a narrow band gap in the spectrum of mode frequencies. Most treatments of photonic band gap materials are based on the true modes, obtained numerically by solving the Helmholtz equation for the actual spatially periodic permittivity. Here the field modes are first treated in terms of a simpler quasimode approach, in which the quasimodes are plane waves associated with the constant permittivity term. Couplings between the quasimodes occur owing to the small periodic term in the permittivity, with selection rules for the coupled modes being related to the reciprocal lattice vectors. This produces a field Hamiltonian in quasimode form. A matrix diagonalization method may be applied to relate true mode annihilation operators to those for quasimodes. The atomic transitions are coupled to all the quasimodes, and the true mode atom-EM field coupling constants (one-photon Rabi frequencies) are related to those for the quasimodes and also expressions are obtained for the true mode density. The results for the one-photon Rabi frequencies differ from those assumed in other work. Expressions for atomic decay rates are obtained using the Fermi Golden rule, although these are valid only well away from the band gaps.