Motional entanglement in low-energy collisions near shape resonances

Abstract

Einstein, Podolsky, and Rosen discussed their paradox in terms of measuring the positions or momenta of two particles. These degrees of freedom can become entangled upon scattering, but how much entanglement can be created in this process? Here we address this question using 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, we find that the entanglement scales linearly with the scattering cross section, including strong enhancement near shape resonances, for sufficiently narrow initial momentum dispersion. We highlight the differences between scattering in one and higher spatial dimensions and discuss how the generation of motional entanglement can be detected in experiments. Our results open the way to probing, controlling, and eventually using entanglement in quantum collisions.