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Light localization and superradiance

Sajeev John, Minesh P. Mehta

Published Dec 31, 1993• 0 citations
OpenAlex

Abstract

This paper reports results for the Dicke model of superradiance with an infinite-range hopping among a collection of two-level impurity atoms embedded in a photonic band gap dielectric. The phase diagram of such a system supports a transition to a superfluid-like state, which is characterized by the spontaneous generation of polarization in the electromagnetic field mode. This paper also examine the effects of disorder on the phase diagram, and the authors discuss briefly some technological applications.

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This paper reports results for the Dicke model of superradiance with an infinite-range hopping among a collection of two-level impurity atoms embedded in a photonic band gap dielectric. The phase diagram of such a system supports a transition to a superfluid-like state, which is characterized by the spontaneous generation of polarization in the electromagnetic field mode. This paper also examine the effects of disorder on the phase diagram, and the authors discuss briefly some technological applications.
The present state of theoretical and experimental research on collective spontaneous emission (superradiance) in a system of radiators (atoms, molecules, or nuclei) is reviewed. The distinction between superradiance and the amplification of spontaneous emission is discussed. There is also a discussion of conditions under which the effect can be observed and of various theoretical methods for describing superradiance: the quantum single-mode and multimode models and the semiclassical approach. Theoretical papers on superradiance in systems with dimensions smaller than the wavelength of the radiation and also in extended systems are reviewed. It is shown that superradiance may occur in weakly amplifying media. A situation in which the superradiance is oscillatory is described. The possible use of superradiance to generate coherent emission in the x-ray and ? ranges is discussed. The superradiance accompanying Raman scattering of light in atomic and molecular media is studied. The theoretical results are compared with experimental observations of superradiance in the optical range. In an appendix, the nature of the phase transition in a system of radiators interacting through an electromagnetic field is discussed.
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 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.
In the first part of this introductory review we outline the developments in photonic band gap materials from the physics of photonic band gap formation to the fabrication and potential applications of photonic crystals. We briefly describe the analogies between electron and photon localization, present a simple model of a band structure calculation and describe some of the techniques used for fabricating photonic crystals. Also some applications in the field of photonics and optical circuitry are briefly presented. In the second part, we discuss the consequences for the interaction between an atom and the light field when the former is embedded in photonic crystals of a specific type, exhibiting a specific form of a gap in the density of states. We first briefly review the standard treatment (Weisskopf – Wigner theory) in describing the dynamics of spontaneous emission in free space from first principles, and then proceed by explaining the alterations needed to properly treat the case of a two-level atom embedded in a photonic band gap material.
We extend the idea of quantum phase transitions of light in an atom-photon system with a Dicke-Bose-Hubbard model for an arbitrary number of two-level atoms. The formulations of eigenenergies, effective Rabi frequencies, and critical chemical potentials for two atoms are derived. With a self-consistent method, we obtain a complete phase diagram for two two-level atoms on resonance, which indicates the transition from Mott insulator to superfluidity and with a mean excitations diagram for confirmation. We illustrate the generality of the method by constructing the dressed-state basis for an arbitrary number of two-level atoms. In addition, we show that the Mott insulator lobes in the phase diagrams will smash out with the increase of atom numbers. The results of this work provide a step for studying the effects with combinations of Dicke-like and Hubbard-like models to simulate strongly correlated electron systems using photons.
The Dicke model is a paradigmatic quantum-optical model describing the interaction of a collection of two-level systems with a single bosonic mode. Effective implementations of this model made it possible to observe the emergence of superradiance, i.e., cooperative phenomena arising from the collective nature of light-matter interactions. Via reservoir engineering and analogue quantum simulation techniques, current experimental platforms allow us not only to implement the Dicke model but also to design more exotic interactions, such as the two-photon Dicke model. In the Hamiltonian case, this model presents an interesting phase diagram characterized by two quantum criticalities: a superradiant phase transition and a spectral collapse, that is, the coalescence of discrete energy levels into a continuous band. Here, we investigate the effects of both qubit and photon dissipation on the phase transition and on the instability induced by the spectral collapse. Using a mean-field decoupling approximation, we analytically obtain the steady-state expectation values of the observables signaling a symmetry breaking, identifying a first-order phase transition from the normal to the superradiant phase. Our stability analysis unveils a very rich phase diagram, which features stable, bistable, and unstable phases depending on the dissipation rate.