  Holography exploits the interference of light fields to obtain a systematic
reconstruction of the light fields wavefronts. Classical holography techniques
have been very successful in diverse areas such as microscopy, manufacturing
technology, and basic science. Extending holographic methods to the level of
single photons has been proven challenging, since applying classical holography
techniques to this regime pose technical problems. Recently the retrieval of
the spatial structure of a single photon, using another photon under
experimental control with a well-characterized spatial shape as reference, was
demonstrated using the intrinsically non-classical Hong-Ou-Mandel interference
on a beam splitter. Here we present a method for recording a hologram of single
photons without detecting the photons themselves, and importantly, with no need
to use a well-characterized companion reference photon. Our approach is based
on quantum interference between two-photon probability amplitudes in a
nonlinear interferometer. As in classical holography, the hologram of a single
photon allows retrieving the complete information about the "shape" of the
photon (amplitude and phase) despite the fact that the photon is never
detected.
