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Physical Review A

Spontaneous emission from a two-level atom in a three-dimensional photonic crystal

Yaping Yang, Shi-Yao Zhu

Published Jun 12, 2000• 76 citations
Publisher

Abstract

We investigate spontaneous emission from a two-level atom embedded in a photonic crystals with three-dimensional dispersion relation, where the dependence of wave vectors on direction is taken into account. Due to the difference of the density of states of electromagnetic modes between a three-dimensional and a one-dimensional photonic crystal (lack of singularity), the dynamics of the population in the excited state and the emitted field are quite different from those of a one-dimensional photonic crystal. There is no quasi-oscillation for the population evolution. The localized field and the propagating field cannot coexist. When the upper level moves from the gap to the band, the emitted field changes from a localized field to a diffusion field and then to a propagating field. The energy of the diffusion and propagating fields propagates out incoherently and coherently, respectively. An analytical expression for the Lamb shift is obtained. The Lamb shift for the current case is smaller than that in an ordinary vacuum or in one-dimensional photonic crystals.

DOI
10.1103/physreva.62.013805

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Spontaneous emission from a two-level atom embedded in photonic crystals was investigated in this paper. Due to the photon localization and the quantum interference between the two dressed states, some changes in the radiation field take place: when the excited level moves from the gap to the band, the energy of the localized field is transferred to the propagating field through the diffusion field. If the localized field and the propagating field could coexist, the population evolution in the excited level would exhibit quasi-oscillation behavior. If they could not coexist, there would be no quasi-oscillation. The steady-state trapped atom population in the excited level is changed also. All these characteristics depend not only on the relative position δ of the excited level ω _1 with respect to the band-edge ω _c but also on the photon density of states ρ(ω_k) (or the band-edge smoothing parameter e ) near the band edge.
Spontaneous emission in photonic crystals with anisotropic three-dimensional dispersion relation is studied. If the upper level is below a characteristic frequency omega(1), or above omega(2), or between omega(1) and omega(2), the radiation is a localized field with a frequency in the band gap, or a propagating field with a frquency in the band, or a diffusion field, respectively. An analytical expression for the Lamb shift is obtained. The Lamb shift for the current case is small compared to that in an ordinary vacuum or in one- or two-dimensional photonic crystals due to lower density of states.
We have studied the properties of the spontaneous emission from a two-level atom embedded in two-band photonic crystals. Due to the anisotropic two-band dispersion relation, the localized and propagating fields cannot coexist, this leads to the non-quasi-oscillation behaviour of the upper level population. Thus the upper level population will tend to a constant as time goes to infinity, or decay with time in a power law, or decay with time exponentially, different from that in the isotropic one-band dispersion relation case. These properties are directly related to the relative position of the upper level from the band edge and the width of the gap.
We investigate spontaneous emission from a two-level atom embedded in photonic crystals. Due to the photon localization and the quantum interference between the two dressed states, some changes of the radiation field happen, and the energy is transferred among the excited atom, the localized field, the propagating field and the diffusion field. If there is a localized field, it appears quasi-oscillation behaves of the population evolution in the excited level. If there isn't a localized field, it appears no quasi-oscillation. Moreover, there have some steady-state trapped atom populations in the excited level, and the spontaneous emission spectrum near the forbidden gap edge is different from that in the vacuum. All these characteristics depend not only on the relative position of the excited level from the band-edge but also on the photon density of states (or the band-edge smoothing parameter) near the band edge.
We investigate the spontaneous radiation from a two-level atom embedded in a three-dimensional anisotropic photonic crystal with two bands. The properties of the spontaneous emission are dependent strongly on the position of the upper level. The faster and slower decay components can occur in the emitted field, but it does not mean the existence of both accelerated and inhibited components for the atomic population decay. The radiation spectrum is dependent on the location of the observer. We also study the influence of the existence of the two bands on spontaneous emission, Lamb shift, the emitted field, and the radiation spectrum.