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

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. Copyright (C) EPLA, 2009