Mesoscopic steerable superposition states and Einstein-Podolsky-Rosen steering in a Bose-Einstein condensate

In 1935, Einstein, Podolsky and Rosen (EPR) presented their “paradox” that established inconsistency between the completeness of quantum mechanics and local realism. States that show an EPR paradox are called EPR-steerable. We present experimental evidence for genuinely steerable states involving thousands of atoms. Using theory based on superselection rules, we analyze experiments where atoms are cooled to form a Bose-Einstein condensate (BEC). We show that large groups of atoms become indistinguishable particles occupying two distinguishable modes that are EPR-steerable.
The steerable modes are created in a BEC atom interferometer. We construct a full, three-dimensional finite temperature quantum model of the experiment. In this way, we extract the time-evolving condensate fraction and a two-mode correlation moment that we show is a signature of EPR-steering. The value of the moment places a lower bound on the number of atoms comprising the steerable state. By analysing the higher-order structure of the correlations, we confirm entangled superpositions of states with different masses. Assuming the modes can be further separated and local measurements performed, this gives a first step towards mesoscopic steerable superpositions of states with distinct centre-of-mass locations.