Two-dimensional characterization of spatially entangled photon pairs

We characterize the entanglement in position and momentum of photon pairs generated in type-II parametric down-conversion. Coincidence maps of the photon positions in the near-field and far-field planes are observed in two transverse dimensions using scanning fiber probes. We estimate the covariance matrix of an effective two-mode system and apply criteria for entanglement based on covariance matrices to certify space–momentum entanglement. The role of higher-order spatial modes for observing spatial entanglement between the two photons is discussed.