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Intense efforts have been made in recent years to realize nonlinear opticalinteractions at the single-photon level. Much of this work has focused onachieving strong third-order nonlinearities, such as by using single atoms orother quantum emitters while the possibility of achieving strong second-ordernonlinearities remains unexplored. Here, we describe a novel technique torealize such nonlinearities using graphene, exploiting the strong per-photonfields associated with tightly confined graphene plasmons in combination withspatially nonlocal nonlinear optical interactions. We show that in properlydesigned graphene nanostructures, these conditions enable extremely stronginternal down-conversion between a single quantized plasmon and an entangledplasmon pair, or the reverse process of second harmonic generation. A separateissue is how such strong internal nonlinearities can be observed, given thenominally weak coupling between these plasmon resonances and free-spaceradiative fields. On one hand, by using the collective coupling to radiation ofnanostructure arrays, we show that the internal nonlinearities can manifestthemselves as efficient frequency conversion of radiative fields at extremelylow input powers. On the other hand, the development of techniques toefficiently couple to single nanostructures would allow these nonlinearprocesses to occur at the level of single input photons.

Second-order quantum nonlinear optical processes in single graphene nanostructures and arrays