Motional entanglement in low-energy collisions near shape resonances

Einstein, Podolsky, and Rosen discussed their paradox in terms of measuring the positions or momenta of two particles. These can become entangled upon scattering, but how much entanglement can be created in this process? Here we address this question with fully coherent calculations of bipartite scattering in three-dimensional space, quantifying entanglement by the inverse of the single particle purity. We show that the standard plane-wave description of scattering fails to capture the entanglement properties, due to the essential role of quantum uncertainty in the initial state. For a more realistic description of a scattering setup and narrow initial momentum dispersion, we find the entanglement to scale linearly with the scattering cross section, including strong enhancement close to shape resonances. We discuss how the generation of motional entanglement can be detected in experiments. Our results open the way to probing and eventually using entanglement in quantum collisions.