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Condensed matter systems are potential candidates to realize the integrationof quantum information circuits. Surface phonon polariton (SPhP) is a specialpropagation mode in condensed matter systems. We present an investigation onthe entanglement of SPhP modes. The entangled pairs are generated fromentangled photons injected to the system. Quantum performances of entangledSPhPs are investigated by using the interaction Hamiltonian and theperturbation theory. The wave mechanics approach is taken to describe thecoupling process as a comparison. Finally, the correlation of system isexamined. A whole set of descriptions of SPhP entanglement thus are presented.

Quantum entanglement based on surface phonon polaritons in condensed matter systems