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arXiv:1103.2949 · Physical Review A

Lifetime and emission characteristics of collective electronic excitations in two-dimensional optical lattices

Hashem Zoubi, Helmut Ritsch

Published Jun 23, 2011• 25 citations
arXivHTMLPDF

Abstract

Collective electronic excitations in planar optical lattices exhibit strong modifications of the radiative damping rate and directional emission pattern as compared to a single excited atom. Collective excitations for long wave numbers and polarizations orthogonal to the lattice plane exhibit superradiance with a very short lifetime and a tightly confined emission direction. For shorter wavelength and in-plane polarization, they can possess a long lifetime, which, beyond a critical wave number, tends to infinity. Those excitations thus become metastable and decoupled from the free radiation field. They can store a single energy quantum for a long time and transfer the excitation over long distances. In general the spatial, polarization, and frequency dependence of the emission pattern can provide us with optical and electronic properties of optical lattices.

DOI
10.1103/physreva.83.063831

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Collective electronic excitations in planar optical lattices exhibit strong modifications of the radiative damping rate and directional emission pattern as compared to a single excited atom. Collective excitations for long wave numbers and polarizations orthogonal to the lattice plane exhibit superradiance with a very short lifetime and a tightly confined emission direction. For shorter wavelength and in-plane polarization, they can possess a long lifetime, which, beyond a critical wave number, tends to infinity. Those excitations thus become metastable and decoupled from the free radiation field. They can store a single energy quantum for a long time and transfer the excitation over long distances. In general the spatial, polarization, and frequency dependence of the emission pattern can provide us with optical and electronic properties of optical lattices.
The radiative damping rate and light emission pattern of electronic excitons in an infinite one-dimensional chain of atoms strongly deviates from independent atom excitations. Exciton emission in the far field is concentrated in cones centered around the chain. Long-wavelength excitons exhibit superradiance with excitation life time orders of magnitude shorter than a single atom. Short-wavelength excitons show reduced spontaneous emission depending on their polarization and beyond a critical wave number they even can get metastable with zero radiation damping rate. Such meta-stable excitations can propagate and mediate interactions over large distances or store photons in the lattice for a long time. While they cannot be directly optically excited, they can be created and read out via tailored evanescent fields from a nearby structured surface or an optical fiber.
Using Ewald's summation method, we investigate collective electronic excitations (excitons) of ultracold atoms in parallel planar optical lattices including long-range interactions. The exciton dispersion relation can then be suitably rewritten and efficiently calculated for long-range resonance dipole–dipole interactions. Such in-plane excitons resonantly couple for two identical optical lattices, with an energy transfer strength decreasing exponentially with the distance between the lattices. This allows a restriction of the transfer to neighbouring planes and gives rise to excitons delocalized between the lattices. In general, equivalent results will hold for any planar system containing lattice layers of optically active and dipolar materials.
Ultracold atoms uniformly filling an optical lattice can be treated like an artificial crystal. An implementation including the atomic occupation of a single excited atomic state can be represented by a two-component Bose-Hubbard model. Its phase diagram exhibits a quantum phase transition from a superfluid to a Mott insulator phase. The dynamics of electronic excitations governed by electrostatic dipole-dipole interactions in the ordered regime can be well described by wave-like collective excitations called excitons. Here we present an extensive study of such excitons for a wide range of geometries and dimensionality. Their lifetimes can vary over many orders of magnitude from metastable propagation to superradiant decay. Particularly strong effects occur in one dimensional atomic chains coupled to tapered optical fibers. For an optical lattice within a cavity the excitons are coupled to cavity photons and the resulting collective cavity QED model can be efficiently formulated in terms of polaritons. Their properties are explicitly calculated for different lattices and they constitute a non-destructive monitoring tool for important system properties. Even the formation of molecules in optical lattices manifests itself in modified polariton properties as e.g. an anisotropic optical spectrum. Partial dissipation of the exciton energy in the lattice leads to heating, which can be microscopically understood through a mechanism transferring atoms into higher Bloch bands via a resonant excitation transfer among neighboring lattice sites. The presence of lattice defects like vacancies in the Mott insulator induces a characteristic scattering of polaritons, which can be optically observed to monitor the lattice integrity. Our models can be applied to simulate and understand corresponding collective phenomena in solid crystals, where many effects are often masked by noise and disorder.
We study the collective radiation properties of cold, trapped ensembles of atoms. We consider the high-density regime with the mean interatomic distance being comparable to, or smaller than, the wavelength of the resonant optical radiation emitted by the atoms. We find that the emission rate of a photon from an excited atomic ensemble is strongly enhanced for an elongated cloud. We analyze collective single-excitation eigenstates of the atomic ensemble and find that the absorption-emission spectrum is broadened and shifted to lower frequencies as compared to the noninteracting (low-density) or single-atom spectrum. We also analyze the spatial and temporal profile of the emitted radiation. Finally, we explore how to efficiently excite the collective superradiant states of the atomic ensemble from a long-lived storage state in order to implement matter-light interfaces for quantum computation and communication applications.
We introduce a straightforward quantum-electrodynamic approach to the problem of superradiant spontaneous emission from a system of two-level atoms, and also discuss two classical superradiant systems. The same physical concepts underlie our treatment of both the quantum and classical cases. Explicit expressions are found which describe the time evolution and directional character of the radiated power. Our approach applies to an arbitrary number of atoms which are confined to a region with linear dimensions which may be large compared with the mean wavelength of the emitted radiation. The radiative decay half-life of a large many-atom system is found to be much shorter than the natural lifetime of a single atom, but not as short as the half-life of a small atomic system with the same number of atoms. The far-field radiation pattern appropriate to the case of a circular cylinder of emitters which have been excited by a plane-wave pulse is considered in detail. Polar plots are presented of the radiation patterns produced when the atoms are excited by a plane-wave pulse. Exciting pulses traveling in directions both parallel and at an angle of 10\ifmmode^\circ\else\textdegree\fi{} to the axis of the cylinder are considered. A discussion and generalization of Dicke's "coherence-brightening" criterion is given.
The radiative properties of collective electronic states for a finite one-dimensional atomic chain are investigated. The influence of the chain size on the collective damping rates is examined through the dependence on both the chain length and the lattice constant. The symmetric state damping rate is shown to grow up linearly with the length for short chains, in relative to the atomic transition wavelength, and to saturate for long ones. For large lattice constants the saturation is achieved for small number of chain atoms, and vice versa for small ones. The results can be adopted for any chain of active materials, e.g. , an array of quantum dots or organic molecules on a linear matrix.