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Physical Review Letters

Localization of Superradiance near a Photonic Band Gap

Sajeev John, Tran Quang

Published Apr 24, 1995• 287 citations
Publisher

Abstract

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.

DOI
10.1103/physrevlett.74.3419

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We describe collective spontaneous emission of NNN 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 N2/3{N}^{2/3}N2/3 and N2{N}^{2}N2 for isotropic and anisotropic 3D band gaps, respectively. The corresponding peak intensity of superradiance is proportional to N5/3{N}^{5/3}N5/3 and N3{N}^{3}N3, respectively.
We study spontaneous emission near the edge of a photonic band gap. Instead of a simple exponential decay in the vacuum, spontaneous emission displays an oscillatory behavior. A single photon-atom bound dressed state exhibits a fractional steady-state atomic population on the excited state. For a three-level atom we evaluate the spectral splitting and subnatural linewidth of spontaneous emission. In the presence of N-1 unexcited atoms we show that the collective time scale factor is equal to ${\mathit{N}}^{\mathrm{\ensuremath{\varphi}}}$, where \ensuremath{\varphi}=2/3 for an isotropic band gap and \ensuremath{\varphi}=1 or 2 for anisotropic two-dimensional or three-dimensional band edges, respectively.
We discuss a point model for the collective emission of light from NNN two-level atoms in a photonic band-gap material, each with an atomic resonant frequency near the edge of the gap. In the limit of a low initial occupation of the excited atomic state, our system is shown to possess atomic spectra and population statistics that are radically different from free space. For a high initial excited-state population, mean-field theory suggests a fractionalized inversion and a macroscopic polarization for the atoms in the steady state, both of which can be controlled by an external dc field. This atomic steady state is accompanied by a nonzero expectation value of the electric field operators for field modes located in the vicinity of the atoms. The nature of homogeneous broadening near the band edge is shown to differ markedly from that in free space due to non-Markovian memory effects in the radiation dynamics. Non-Markovian vacuum fluctuations are shown to yield a partially coherent steady-state polarization with a random phase. In contrast with the steady state of a conventional laser, near a photonic band edge this coherence occurs as a consequence of photon localization in the absence of a conventional cavity mode. We also introduce a classical stochastic function with the same temporal correlations as the electromagnetic reservoir, in order to stochastically simulate the effects of vacuum fluctuations near a photonic band edge.
We demonstrate the coherent control of spontaneous emission for a three-level atom located within a photonic band gap (PBG) material, with one resonant frequency near the edge of the PBG. Spontaneous emission from the three-level atom can be totally suppressed or strongly enhanced depending on the relative phase between the steady-state control laser coupling the two upper levels and the pump laser pulse used to create an excited state of the atom in the form of a coherent superposition of the two upper levels. Unlike the free-space case, the steady-state inversion of the atomic system is strongly dependent on the externally prescribed initial conditions. This non-zero steady-state population is achieved by virtue of the localization of light in the vicinity of the emitting atom. It is robust to decoherence effects provided that the Rabi frequency of the control laser field exceeds the rate of dephasing interactions. As a result, such a system may be relevant for a single-atom, phase-sensitive optical memory device on the atomic scale. The protected electric dipole within the PBG provides a basis for a qubit to encode information for quantum computations. A detailed literature survey on the nature, fabrication and applications of PBG materials is presented to provide context for this research.
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.
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.