  Condensed matter systems are potential candidates to realize the integration
of quantum information circuits. Surface phonon polariton (SPhP) is a special
propagation mode in condensed matter systems. We present an investigation on
the entanglement of SPhP modes. The entangled pairs are generated from
entangled photons injected to the system. Quantum performances of entangled
SPhPs are investigated by using the interaction Hamiltonian and the
perturbation theory. The wave mechanics approach is taken to describe the
coupling process as a comparison. Finally, the correlation of system is
examined. A whole set of descriptions of SPhP entanglement thus are presented.
