Hologram of a single photon

The spatial structure of single photons(1-3) is becoming an extensively explored resource to facilitate free-space quantum communication(4-7) and quantum computation(8) as well as for benchmarking the limits of quantum entanglement generation(3) with orbital angular momentum modes(1,9) or reduction of the photon free-space propagation speed(10). Although accurate tailoring of the spatial structure of photons is now routinely performed using methods employed for shaping classical optical beams(3,10,11), the reciprocal problem of retrieving the spatial phase-amplitude structure of an unknown single photon cannot be solved using complementary classical holography techniques(12,13) that are known for excellent interferometric precision. Here, we introduce a method to record a hologram of a single photon that is probed by another reference photon, on the basis of a different concept of the quantum interference between two-photon probability amplitudes. As for classical holograms, the hologram of a single photon encodes the full information about the photon's 'shape' (that is, its quantum wave function) whose local amplitude and phase are retrieved in the demonstrated experiment.