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We consider a generation of two-particle quantum states in the process ofspontaneous parametric down-conversion of light by a dielectric nanoparticlewith $\chi^{(2)}$ response. As a particular example, we study the generation ofsurface plasmon-polariton pairs with a ${\rm GaAs}$ nanoparticle located at thesilver-air interface. We show that for certain excitation geometries, ${\rmN00N}$-states of surface plasmon-polariton pairs could be obtained. The effectcan be physically interpreted as a result of quantum interference between pairsof induced sources, each emitting either signal or idler plasmon. We thenrelate the resulting ${\rm N00N}$-pattern to the general symmetry properties ofdyadic Green's function of a dipole emitter exciting surface waves. It rendersthe considered effect as a general way towards a robust generation of ${\rmN00N}$-states of surface waves using spontaneous parametric down-conversion in$\chi^{(2)}$ nanoparticles.

Generating ${\rm N00N}$-states of surface plasmon-polariton pairs with a nanoparticle