Optics and Spectroscopy

Superradiant decay of localized excitations in a linear atomic chain

E. A. Gavrilenko, А. И. Зайцев

Published Mar 1, 2009• 0 citations

Abstract

The superradiant decay of localized excitations in a linear chain of two-level atoms has been investigated. It is shown that the excitation energy is not completely emitted in the cooperative stage of the process. The residual excitation forms waves propagating from the regions of initial localization to the chain edges.

DOI: 10.1134/s0030400x09030035

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Optics and Spectroscopy

Superradiant decay of localized excitations in a linear atomic chain

E. A. Gavrilenko, А. И. Зайцев

Published Mar 1, 2009• 0 citations

Publisher

Abstract

DOI: 10.1134/s0030400x09030035

Related papers

Super-radiance and decay localized excitations in the linear equidistant system of N two-level atoms

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Sajeev John, Tran Quang

We describe collective spontaneous emission of $N$ two-level atoms placed within a photonic band-gap material. When the atomic resonance frequency lies at the band edge, superradiant emission remains localized in the vicinity of the atoms. This leads to a steady state with spontaneously broken symmetry in which the atomic system acquires a macroscopic polarization. The superradiant decay rate is proportional to ${N}^{2/3}$ and ${N}^{2}$ for isotropic and anisotropic 3D band gaps, respectively. The corresponding peak intensity of superradiance is proportional to ${N}^{5/3}$ and ${N}^{3}$ , respectively.We describe collective spontaneous emission of $N$ two-level atoms placed within a photonic band-gap material. When the atomic resonance frequency lies at the band edge, superradiant emission remains localized in the vicinity of the atoms. This leads to a steady state with spontaneously broken symmetry in which the atomic system acquires a macroscopic polarization. The superradiant decay rate is proportional to ${N}^{2/3}$ and ${N}^{2}$ for isotropic and anisotropic 3D band gaps, respectively. The corresponding peak intensity of superradiance is proportional to ${N}^{5/3}$ and ${N}^{3}$, respectively.

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The radiation pattern of light scattered from a chain of atoms having $J=0$ ground states and $J=1$ excited states is calculated in the weak driving field approximation. It is shown that, in general, for arbitrary orientation of the driving field to the chain axis, it is not possible to treat the atoms in a two-level approximation owing to cooperative effects. In the limit of large detuning, however, all cooperative decay effects can be neglected in calculating the scattered spectrum. Nevertheless, even in this limit, in order to ensure conservation of energy, it is still necessary to include cooperative decay when calculating the energy lost by the driving field. For arbitrary detunings, conservation of energy can be expressed in the form of a generalized optical theorem.The radiation pattern of light scattered from a chain of atoms having $J=0$ ground states and $J=1$ excited states is calculated in the weak driving field approximation. It is shown that, in general, for arbitrary orientation of the driving field to the chain axis, it is not possible to treat the atoms in a two-level approximation owing to cooperative effects. In the limit of large detuning, however, all cooperative decay effects can be neglected in calculating the scattered spectrum. Nevertheless, even in this limit, in order to ensure conservation of energy, it is still necessary to include cooperative decay when calculating the energy lost by the driving field. For arbitrary detunings, conservation of energy can be expressed in the form of a generalized optical theorem.

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Q

cavity so fast that they cannot feed themselves back into atomic excitation to any appreciable amount (this no-feedback condition is equivalent to the above-mentioned requirement for the length of the sample). (ii) The incoherent atomic decay due to natural relaxation is so slow that the individual atomic dipoles do not dephase before engaging themselves cooperatively in the interaction with the electromagnetic field. The present paper presents the derivation and general discussion of the equations describing the statistical properties of atoms and field in a superradiant pulse. Analytical and numerical solutions will be presented in a subsequent paper.

We describe collective spontaneous emission of

N

two-level atoms placed within a photonic band-gap material. When the atomic resonance frequency lies at the band edge, superradiant emission remains localized in the vicinity of the atoms. This leads to a steady state with spontaneously broken symmetry in which the atomic system acquires a macroscopic polarization. The superradiant decay rate is proportional to

{N}^{2/3}

and

{N}^{2}

for isotropic and anisotropic 3D band gaps, respectively. The corresponding peak intensity of superradiance is proportional to

{N}^{5/3}

and

{N}^{3}

, respectively.

The radiation pattern of light scattered from a chain of atoms having

J=0

ground states and

J=1

excited states is calculated in the weak driving field approximation. It is shown that, in general, for arbitrary orientation of the driving field to the chain axis, it is not possible to treat the atoms in a two-level approximation owing to cooperative effects. In the limit of large detuning, however, all cooperative decay effects can be neglected in calculating the scattered spectrum. Nevertheless, even in this limit, in order to ensure conservation of energy, it is still necessary to include cooperative decay when calculating the energy lost by the driving field. For arbitrary detunings, conservation of energy can be expressed in the form of a generalized optical theorem.