  A lattice of trapped atoms strongly coupled to a one-dimensional nanophotonic
waveguide is investigated in exploiting the concept of polariton as the system
natural eigenstate. We apply a bosonization procedure, which was presented
separately by P. W. Anderson and V. M. Agranovich, to transform excitation
spin-half operators into interacting bosons, and which shown here to confirm
the hard-core boson model. We derive polariton-polariton kinematic interactions
and study them by solving the scattering problem. In using the
excitation-photon detuning as a control parameter, we examine the regime in
which polaritons behave as weakly interacting photons, and propose the system
for realizing superfluidity of photons. We implement the kinematic interaction
as a mechanism for nonlinear optical processes that provide an observation tool
for the system properties, e.g. the interaction strength produces a blue shift
in pump-probe experiments.

Quantum Physics