Collective excitations in circular atomic configurations and single-photon traps

Abstract

Correlated excitations in a plane circular configuration of identical atoms with parallel dipole moments are investigated. The collective energy eigenstates, which are formally identical to Frenkel excitons, can be computed together with their level shifts and decay rates by decomposing the atomic state space into carrier spaces for the irreducible representations of the symmetry group Z{sub N} of the circle. It is shown that the index p of these representations can be used as a quantum number analogously to the orbital angular momentum quantum number l in hydrogenlike systems. Just as the hydrogen s states are the only electronic wave functions which can occupy the central region of the Coulomb potential, the quasiparticle corresponding to a collective excitation of the atoms in the circle can occupy the central atom only for vanishing Z{sub N} quantum number p. If a central atom is present, the p=0 state splits into two and shows level crossing at certain radii; in the regions between these radii, damped quantum beats between two 'extreme' p=0 configurations occur. The physical mechanisms behind super- and subradiance at a given radius are discussed. It is shown that, beyond a certain critical number of atoms in the circle, the lifetimemore » of the maximally subradiant state increases exponentially with the number of atoms in the configuration, making the system a natural candidate for a single-photon trap.« less