Detecting entanglement in spatial interference.

We discuss an experimentally amenable class of two-particle states of motion giving rise to nonlocal spatial interference under position measurements. Using the concept of modular variables, we derive a separability criterion which is violated by these non-Gaussian states. While we focus on the free motion of material particles, the presented results are valid for any pair of canonically conjugate continuous variable observables and should apply to a variety of bipartite interference phenomena.