Plasmon-assisted Quantum Entanglement

The state of a two-particle system is called entangled when its quantum mechanical wave function cannot be factorized in two single-particle wave functions. Entanglement leads to the strongest counter-intuitive feature of quantum mechanics, namely nonlocality. Experimental realization of quantum entanglement is relatively easy for the case of photons; a pump photon can spontaneously split into a pair of entangled photons inside a nonlinear crystal. In this paper we combine quantum entanglement with nanostructured metal optics in the form of optically thick metal films perforated with a periodic array of subwavelength holes. These arrays act as photonic crystals that may convert entangled photons into surface-plasmon waves, i.e., compressive charge density waves. We address the question whether the entanglement survives such a conversion. We find that, in principle, optical excitation of the surface plasmon modes of a metal is a coherent process at the single-particle level. However, the quality of the plasmon-assisted entanglement is limited by spatial dispersion of the hole arrays. This spatial dispersion is due to the nonlocal dielectric response of a metal, which is particularly large in the plasmonic regime; it introduces "which way" labels, that may kill entanglement.