Quantum entanglement based on surface phonon polaritons in condensed matter systems

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 SPhP pairs are generated through launching entangled photons onto the grating coupling systems. The interaction Hamiltonian for the coupling process between entangled photons and entangled LRSPhPs is derived. State vector of the entangled LRSPhPs is obtained through the perturbation theory. The origin of LRSPhP entanglement is revealed. Wave mechanics approach is taken to describe the coupling process as an alteration. To present the nonlocality, the second-order correlation function is studied.