Issue
EPL
Volume 87, Number 2, July 2009
Article Number 23001
Number of page(s) 5
Section Atomic, Molecular and Optical Physics
DOI http://dx.doi.org/10.1209/0295-5075/87/23001
Published online 07 August 2009
EPL, 87 (2009) 23001
DOI: 10.1209/0295-5075/87/23001

Superradiant and dark exciton states in an optical lattice within a cavity

H. Zoubi and H. Ritsch

Institut fur Theoretische Physik, Universitat Innsbruck - Technikerstrasse 25, A-6020 Innsbruck, Austria, EU

hashem.zoubi@uibk.ac.at

received 12 June 2009; accepted in final form 10 July 2009; published July 2009
published online 7 August 2009

Abstract
We study ultracold atoms trapped in a one-dimensional optical lattice prepared in a Mott insulator state of finite extend and collectively coupled to a single cavity mode. Due to resonant dipole-dipole interactions among the atoms, electronic excitations get delocalized and form excitons. These excitons can be explicitly calculated and divided into two groups: antisymmetric modes which decouple from the cavity mode called dark excitons, and symmetric modes coupled to the cavity mode called bright excitons. In a typical geometry the most uniform exciton is coupled to the cavity photons much stronger than other symmetric bright states and dominates the optical response of the atoms (superradiant state). In the strong coupling regime this superradiant state mixes with a cavity photon to form a doublet of polariton states, and the other excitons play only a minor role in the dynamics. We analytically calculate the corresponding collective Rabi splitting including the nearest-neighbor dipole-dipole induced excitonic shifts, which strongly depend on the polarization of the cavity mode with respect to the lattice orientation.

PACS
37.10.Jk - Atoms in optical lattices.
42.50.Pq - Cavity quantum electrodynamics; micromasers.
37.30.+i - Atoms, molecules, and ions in cavities.

© EPLA 2009