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Physical Review Letters

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

Boris Sherman, Gershon Kurizki, A. Kadyshevitch

Published Sep 28, 1992• 25 citations
Publisher

Abstract

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.

DOI
10.1103/physrevlett.69.1927

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

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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.

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Influence of pump-field scattering to nonclassical-light generation in a photonic band-gap nonlinear planar waveguide

Jan Peřina, Concita Sibilia, Daniela Tricca +1 more

Optical parametric process occurring in a nonlinear planar waveguide can serve as a source of light with nonclassical properties. Properties of the generated fields are substantially modified by scattering of the nonlinearly interacting fields in a photonic band-gap structure inside the waveguide. A quantum model of linear operator amplitude corrections to amplitude mean-values provides conditions for an efficient squeezed-light generation as well as generation of light with sub-Poissonian photon-number statistics. Destructive influence of phase mismatch of the nonlinear interaction can fully be compensated using a suitable photonic-band gap structure inside the waveguide. Also an increase of signal-to-noise ratio of an incident optical field can be reached in the waveguide.

arXiv:quant-ph/0412208•Dec 28, 2004•0 citations
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.
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.
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 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.
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.
Optical parametric process occurring in a nonlinear planar waveguide can serve as a source of light with nonclassical properties. Properties of the generated fields are substantially modified by scattering of the nonlinearly interacting fields in a photonic band-gap structure inside the waveguide. A quantum model of linear operator amplitude corrections to amplitude mean-values provides conditions for an efficient squeezed-light generation as well as generation of light with sub-Poissonian photon-number statistics. Destructive influence of phase mismatch of the nonlinear interaction can fully be compensated using a suitable photonic-band gap structure inside the waveguide. Also an increase of signal-to-noise ratio of an incident optical field can be reached in the waveguide.