Quantum Gap Solitons and Many-Polariton–Atom Bound States in Dispersive Medium and Photonic Band Gap

Abstract

A system of polaritons interacting with a two-level atom placed within a frequency dispersive medium is proven to be integrable and diagonalized exactly by the Bethe ansatz method, despite a nonlocal effective polariton-polariton coupling. Its spectrum consists of bound many-polariton complexes (quantum solitons) and exhibits unusual features due to the existence of the polaritonic gap. Only solitons containing an even number of polaritons (``even'' solitons) propagate within the gap, while an ``odd'' soliton is pinned to the atom and forms a many-polariton--atom bound state.