  We consider a semiconductor polymer chain coupled to a single electromagnetic
mode in a cavity. The excitations of the chain have a mixed exciton-photon
character and are described as polaritons. Polaritons are coupled to the
lattice by the deformation potential interaction and can propagate in the
chain. We find that the presence of optical excitation in the polymer induces
strain on the lattice. We use a BCS variational wavefunction to calculate the
chemical potential of the polaritons as a function of their density. We analyze
first the case of a short chain with only two unit cells in order to check the
validity of our variational approach. In the case of a long chain and for a
strong coupling with the lattice, the system undergoes a phase transition
corresponding to the self-trapping of polaritons. The role of the exciton
spontaneous emission and cavity damping are discussed in the case of
homogeneous optical lattice strain.
