Spatial entanglement in interacting Bose-Einstein condensates

The entanglement between spatial regions in an interacting Bose-Einstein condensate is investigated using a quantum field theoretic formalism. Regions that are small compared to the healing length are governed by a nonrelativistic quantum field theory in the vacuum limit, and we show that the latter has vanishing entanglement. In the opposite limit of a region that is large compared to the healing length, the entanglement entropy is like in the vacuum of a relativistic theory where the velocity of light is replaced with the velocity of sound and where the inverse healing length provides a natural ultraviolet regularization scale. Besides the von Neumann entanglement entropy, we also calculate Renyi entanglement entropies for a one-dimensional quasicondensate.

Automated summary

Investigations into spatial regions within an interacting Bose-Einstein condensate using quantum field theory reveal that small regions relative to the healing length exhibit zero entanglement in the vacuum limit, while larger regions show entanglement entropy akin to that in the vacuum of a relativistic theory.