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Electromagnetically Induced Exciton Dynamics and Bose-Einstein Condensation near a Photonic Band Gap

Sheng-Jun Yang

Published Mar 26, 2012• 0 citations
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Abstract

We demonstrate electromagnetically-induced anomalous quantum dynamics of an exciton in a photonic band gap (PBG) - quantum well (QW) hetero-structure. Within the engineered electromagnetic vacuum of the PBG material, the exciton can propagate through the QW by the emission and re-absorption of virtual photons in addition to the conventional electronic hopping mechanism. When the exciton wavevector and recombination energy coincide nearly with a photonic band edge, the exciton kinetic energy is lowered by 1-10meV through coherent radiative hopping. This capture of the exciton by the photonic band edge is accompanied by strong electromagnetic dressing in which the exciton's renormalized effective mass is 4-5 orders of magnitude smaller than in the absence of the PBG environment. This dressed exciton exhibits a long radiative lifetime characteristic of a photon-atom bound state and is robust to phonon-assisted, re-combinative decay. By inheriting properties of the PBG electromagnetic vacuum, the bound electron-hole pair becomes a stable, ultra-mobile quantum excitation. Unlike traditional exciton-polariton modes created by placing a QW in a one-dimensional optical cavity, our PBG-QW excitons exhibit strong coupling to optical modes and retain a long lifetime. This is crucial for unambiguous observation of quantum coherence effects such as Bose-Einstein condensation. We present a model for the equilibrium quantum statistics of a condensate of repulsively interacting bosons in a two-dimensional trap. Particle correlations in the ground state are treated exactly, whereas interactions with excited particles are treated in a generalized Bogoliubov mean-field theory. This leads to a fundamental physical picture for condensation of interacting bosons through an anharmonic oscillator ground state coupled to excited Bogoliubov quasiparticles in which the quantum number statistics of condensate particles emerges self-consistently. Our anharmonic oscillator model for the exciton ground state manifold goes beyond the conceptual framework of traditional Bogoliubov theory. Below the Bose-Einstein condensation temperature, our model exhibits a crossover from particle bunching to Poissonian statistics and finally antibunching as temperature is lowered or as the trapping area is decreased. When applied to Bose condensation of long-lived dressed excitons in a photonic band gap material, our model suggests that this system may serve as a novel tunable source for non-classical states of light.

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Physical review. B, Condensed matter•Jun 1, 1991•395 citations
We demonstrate electromagnetically-induced anomalous quantum dynamics of an exciton in a photonic band gap (PBG) - quantum well (QW) hetero-structure. Within the engineered electromagnetic vacuum of the PBG material, the exciton can propagate through the QW by the emission and re-absorption of virtual photons in addition to the conventional electronic hopping mechanism. When the exciton wavevector and recombination energy coincide nearly with a photonic band edge, the exciton kinetic energy is lowered by 1-10meV through coherent radiative hopping. This capture of the exciton by the photonic band edge is accompanied by strong electromagnetic dressing in which the exciton's renormalized effective mass is 4-5 orders of magnitude smaller than in the absence of the PBG environment. This dressed exciton exhibits a long radiative lifetime characteristic of a photon-atom bound state and is robust to phonon-assisted, re-combinative decay. By inheriting properties of the PBG electromagnetic vacuum, the bound electron-hole pair becomes a stable, ultra-mobile quantum excitation. Unlike traditional exciton-polariton modes created by placing a QW in a one-dimensional optical cavity, our PBG-QW excitons exhibit strong coupling to optical modes and retain a long lifetime. This is crucial for unambiguous observation of quantum coherence effects such as Bose-Einstein condensation. We present a model for the equilibrium quantum statistics of a condensate of repulsively interacting bosons in a two-dimensional trap. Particle correlations in the ground state are treated exactly, whereas interactions with excited particles are treated in a generalized Bogoliubov mean-field theory. This leads to a fundamental physical picture for condensation of interacting bosons through an anharmonic oscillator ground state coupled to excited Bogoliubov quasiparticles in which the quantum number statistics of condensate particles emerges self-consistently. Our anharmonic oscillator model for the exciton ground state manifold goes beyond the conceptual framework of traditional Bogoliubov theory. Below the Bose-Einstein condensation temperature, our model exhibits a crossover from particle bunching to Poissonian statistics and finally antibunching as temperature is lowered or as the trapping area is decreased. When applied to Bose condensation of long-lived dressed excitons in a photonic band gap material, our model suggests that this system may serve as a novel tunable source for non-classical states of light.
We present a model for the equilibrium quantum statistics of a condensate of repulsively interacting bosons in a two-dimensional trap. Particle correlations in the ground state are treated exactly, whereas interactions with excited particles are treated in a generalized Bogoliubov mean-field theory. This leads to a fundamental physical picture for the condensation of interacting bosons through an anharmonic oscillator ground state coupled to excited Bogoliubov quasiparticles in which the quantum number statistics of condensate particles emerges self-consistently. Below the Bose-Einstein condensation temperature, our model exhibits a crossover from particle bunching to Poissonian statistics and finally antibunching as the temperature is lowered or as the trapping area is decreased. When applied to Bose condensation of long-lived dressed excitons in a photonic band gap material, our model suggests that this system may serve as a novel tunable source for nonclassical states of light.
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.
We derive a quantum theory of the role of acoustic and optical phonons in modifying the optical absorption line shape, polarization dynamics, and population dynamics of a two-level atom (quantum dot) in the ``colored'' electromagnetic vacuum of a photonic band-gap (PBG) material. This is based on a microscopic Hamiltonian describing both radiative and vibrational processes quantum mechanically. We elucidate the extent to which phonon-assisted decay limits the lifetime of a single photon-atom bound state and derive the modified spontaneous emission dynamics due to coupling to various phonon baths. We demonstrate that coherent interaction with undamped phonons can lead to an enhanced lifetime of a photon-atom bound state in a PBG. This results in reduction of the steady-state atomic polarization but an increase in the fractionalized upper state population in the photon-atom bound state. We demonstrate, on the other hand, that the lifetime of the photon-atom bound state in a PBG is limited by the lifetime of phonons due to lattice anharmonicities (breakup of phonons into lower energy phonons) and purely nonradiative decay. We also derive the modified polarization decay and dephasing rates in the presence of such damping. This leads to a microscopic, quantum theory of the optical absorption line shapes. Our model and formalism provide a starting point for describing dephasing and relaxation in the presence of external coherent fields and multiple quantum dot interactions in electromagnetic reservoirs with radiative memory effects.
Summary form only given. Unlike semiconductors which facilitate the coherent propagation of electrons, photonic band gap (PBG) materials execute their novel functions through the coherent localization of photons. When a PBG material is doped with impurity atoms which have an electronic transition that lies within the gap, spontaneous emission of light from the atom is inhibited. Inside the gap, the photon forms a bound state to the atom. Outside the gap, radiative dynamics in the colored vacuum is highly nonMarkovian. I discuss the influence of these memory effects on laser action. When spontaneous emission is absent, the next order radiative effect (resonance dipole-dipole interaction between atoms) must be incorporated, leading to anomalous nonlinear optical effects which occur at a much lower threshold than in ordinary vacuum. I describe the collective switching of two-level atoms near a photonic band edge, by external laser field, from a passive stare to one exhibiting population inversion. This effect is forbidden in ordinary vacuum. Finally, I discuss the prospects for a phase sensitive, single (3-level) atom quantum memory device, onto which information may be written by an external laser pulse. By scattering polarized photons (flying qubit) this system may execute certain quantum logic operations.
In this thesis we study the role of nonradiative degrees of freedom on quantum optical properties of mesoscopic quantum dots placed in the structured electromagnetic reservoir of a photonic crystal. We derive a quantum theory of the role of acoustic and optical phonons in modifying the optical absorption lineshape, polarization dynamics, and population dynamics of a two-level atom (quantum dot) in the ``colored" electromagnetic vacuum of a photonic band gap (PBG) material. This is based on a microscopic Hamiltonian describing both radiative and vibrational processes quantum mechanically. Phonon sidebands in an ordinary electromagnetic reservoir are recaptured in a simple model of optical phonons using a mean-field factorization of the atomic and lattice displacement operators. Our formalism is then used to treat the non-Markovian dynamics of the same system within the structured electromagnetic density of states of a photonic crystal. We elucidate the extent to which phonon-assisted decay limits the lifetime of a single photon-atom bound state and derive the modified spontaneous emission dynamics due to coupling to various phonon baths. We demonstrate that coherent interaction with undamped phonons can lead to enhanced lifetime of a photon-atom bound state in a PBG by (i) dephasing and reducing the transition electric dipole moment of the atom and (ii) reducing the quantum mechanical overlap of the state vectors of the excited and ground state (polaronic shift). This results in reduction of the steady-state atomic polarization but an increase in the fractionalized upper state population in the photon-atom bound state. We demonstrate, on the other hand, that the lifetime of the photon-atom bound state in a PBG is limited by the lifetime of phonons due to lattice anharmonicities (break-up of phonons into lower energy phonons) and purely nonradiative decay. We demonstrate how these additional damping effects limit the extent of the polaronic (Franck-Condon) shift of the atomic excited state. We also derive the modified polarization decay and dephasing rates in the presence of such damping. This leads to a microscopic, quantum theory of the optical absorption lineshapes. Our model and formalism provide a starting point for describing dephasing and relaxation in the presence of external coherent fields and multiple quantum dot interactions in electromagnetic reservoirs with radiative memory effects.
We describe the quantum electrodynamics of photons interacting with hydrogenic atoms and molecules in a class of strongly scattering dielectric materials. These dielectrics consist of an ordered or nearly ordered array of spherical scatterers with real positive refractive index and exhibit a complete photonic band gap or pseudogap for all directions of electromagnetic propagation. For hydrogenic atoms with a transition frequency in the forbidden optical gap, we demonstrate both the existence and stability of a photon-atom bound state. For a band gap to center frequency ratio \ensuremath{\Delta}\ensuremath{\omega}/${\mathrm{\ensuremath{\omega}}}_{0}$\ensuremath{\sim}5%, the photon localization length ${\ensuremath{\xi}}_{\mathrm{loc}}$\ensuremath{\ge}10L, where L is the lattice constant of dielectric array. This strong self-dressing of the atom by its own localized radiation field leads to anomalous Lamb shifts and a splitting of the excited atomic level into a doublet when the transition frequency lies near a photonic band edge. We estimate the magnitude of this splitting to be ${10}^{\mathrm{\ensuremath{-}}6}$ at the vacuum transition energies.The stability of this photon-bound state with respect to electromagnetic as well as vibrational decay mechanisms is examined. For an isolated molecule embedded in the solid fraction of the dielectric structure, the dominant mechanism for absorption and spontaneous emission is via optically driven electron-phonon interactions and the resulting phonon-absorption and -emission sidebands. Raman or Brillouin scattering of a localized photon into a propagating mode, or vice versa, directly by photon-phonon interaction is forbidden. For atoms not in contact with the solid fraction of the dielectric host, the electromagnetic two-photon spontaneous emission rate is on the scale of several days. For two identical atoms separated by a distance R within the photonic band gap, energy transfer from an excited atom to an unexcited atom occurs by a phase-shifted resonance dipole-dipole interaction which vanishes exponentially for R>${\ensuremath{\xi}}_{\mathrm{loc}}$. This leads to the formation of a narrow photonic impurity band within the gap when a finite density of atoms is present. This impurity band exhibits a different kind of nonlinear optical properties. When two neighboring atoms are both excited, single-photon spontaneous emission at \ensuremath{\sim}2\ensuremath{\Elzxh}${\mathrm{\ensuremath{\omega}}}_{0}$ occurs by a third-order electromagnetic process with rate \ensuremath{\Gamma}\ensuremath{\sim}${\mathrm{\ensuremath{\alpha}}}^{3}$${\mathrm{\ensuremath{\omega}}}_{0}$(a0{\mathit{a}}_{0}a0​/R)8{)}^{8})8, where a0{\mathit{a}}_{0}a0​ is the atomic Bohr radius and \ensuremath{\alpha} is the fine-structure constant.