Holographic measurement of single photon spatial wavefunction

Summary form only given. The spatial structure of a photon has proved to be indispensable resource allowing the experimental realization of free-space quantum cryptography or high dimensional entanglement. Although efficient methods for manipulating spatial characteristic of individual photons can be easily transferred from the field of classical optics, their spatial structure cannot be measured using the standard interferometric reference-based methods such as optical holography due to their completely undefined-global phase. Hence, the full recovery of a transverse photon wavefunction still remains a challenging task tackled so far exclusively using indirect methods such as the quantum tomography [1] and weak values measurements [2].Here we present and experimentally demonstrate a different approach based on spatially resolved detection of two-photon interference [3,4]. Although such measurements are usually perceived to be insensitive to the relative phase between two interfering photons we show that rarely considered local phase dependence can be still observed and utilized for direct recovery of a single photon quantum wavefunction. In particular we experimentally show that the complex transversal wavefunction of the unknown photon can be fully recovered from the 2D spatial coincidence pattern resulting from its two-photon interference with the reference photon [5].