  Surface plasmon polaritons (plasmons) are a combination of light and a
collective oscillation of the free electron plasma at metal-dielectric
interfaces. This interaction allows sub-wavelength confinement of light, beyond
the diffraction limit inherent to dielectric structures. The resulting
electromagnetic fields are more intense and the strength of optical
interactions between metallic structures and light-sources or detectors can be
increased. Plasmons maintain non-classical photon statistics and preserve
entanglement on plasmon-assisted transmission through thin, patterned metallic
films or weakly confining waveguides. For quantum applications it is essential
that plasmons behave as indistinguishable quantum particles. Here we report on
a quantum interference experiment in a nanoscale plasmonic circuit consisting
of an on-chip plasmon beam splitter with integrated superconducting
single-photon detectors to allow efficient single plasmon detection. We
demonstrate quantum mechanical interaction between pairs of indistinguishable
plasmons by observing Hong-Ou-Mandel interference, a hallmark non-classical
effect which is the basis of linear optics-based quantum computation. Our work
shows that it is feasible to shrink quantum optical experiments to the
nanoscale and demonstrates a promising route for sub-wavelength quantum optical
networks.
