Beyond single-photon localization at the edge of a photonic band gap

Georgios Nikolopoulos, University of Crete, Greece

The theory of excitations in a structured reservoir involving
more than one photon remains an open problem. An approach based on a
discretization technique has been shown capable of handling at least
few photons in structured reservoirs of any density of states(DOS).
An atomic ladder system, with both transitions near resonantly coupled to
the edge of a PBG continuum, involves a cascade of two photons, re-
presenting thus a problem with two photons in a structured reservoir.
Solving the problem through the discretization technique, an exact
description of the dynamics of the system is obtained, and the formation
of a ``two-photon+atom'' bound state is predicted. As a result,
both upper atomic levels exhibit non-zero steady state population and the
atom can be found excited in the long-time limit.
Due to the localization of two photons at the site of the
atom, a direct two-photon process coexists with the stepwise one leading
to a counterintuitive coherent evolution of the three atomic states. The
problem is discussed in the context of two models of DOS for the description
of the PBG continuum.