"Quantum atom optics aims at performing with atoms similar experiments to that performed in quantum optics with photons. The motivation for doing so is twofold. From a fundamental point of view, we wish to demonstrate that non-classical correlations and entanglement exist also for massive particles and behave as predicted by quantum theory. From a more practical point of view, such properties also represent the central resource for quantum computing and a tool to increase the sensitivity of atom interferometers. Yet atoms are much more difficult to manipulate than photons because of their coupling to the environment and there is a long way to go until quantum atom optics catches up with quantum optics.This proposal investigates a new route towards this goal as it focuses on pairs of atoms with an entangled momentum state, in sharp contrast with the vast majority of quantum atom optics experiments so far, which relied on the internal degrees of freedom. More precisely, the research project proposes to generate two atomic beams in a two-mode squeezed state and to probe the entanglement by means of a Mach–Zehnder-like interferometric measurement. In this setup, the spatially separated twin-atom beams will be recombined onto a beam splitter and the two output ports will be monitored by a single-atom detector. The analysis of correlations between the atom number at each port will allow us demonstrating the presence of entanglement. Using mechanical degrees of freedom, we will closely follow the reasoning put forward by Einstein, Podolsky and Rosen, and we be able to demonstrate entanglement in the most “classical” situation."