  Feynman described the double slit experiment as "a phenomenon which is
impossible, absolutely impossible, to explain in any classical way and which
has in it the heart of quantum mechanics". The double slit experiment,
performed one photon at a time, dramatically demonstrates the particle-wave
duality of quantum objects by generating a fringe pattern corresponding to the
interference of light (a wave phenomenon) from two slits, even when there is
only one photon (a particle) at a time passing through the apparatus. The
particle-wave duality of light should also apply to complex three dimensional
optical fields formed by multi-path interference, however, this has not been
demonstrated. Here we observe particle-wave duality of a three dimensional
field by generating a trefoil optical vortex knot - one photon at a time. This
result demonstrates a fundamental physical principle, that particle-wave
duality implies interference in both space (between spatially distinct modes)
and time (through the complex evolution of the superposition of modes), and has
implications for topologically entangled single photon states, orbital angular
momentum multiplexing and topological quantum computing.
