Title: Entanglement and entropy production in coupled single-mode Bose-Einstein condensates,
Abstract: We investigate the time evolution of the entanglement entropy of coupled
single-mode Bose-Einstein condensates in a double well potential at $T=0$
temperature, by combining numerical results with analytical approximations. We
find that the coherent oscillations of the condensates result in entropy
oscillations on the top of a linear entropy generation at short time scales.
Due to dephasing, the entropy eventually saturates to a stationary value, in
spite of the lack of equilibration. We show that this long time limit of the
entropy reflects the semiclassical dynamics of the system, revealing the
self-trapping phase transition of the condensates at large interaction strength
by a sudden entropy jump. We compare the stationary limit of the entropy to the
prediction of a classical microcanonical ensemble, and find surprisingly good
agreement in spite of the non-equilibrium state of the system. Our predictions
should be experimentally observable on a Bose-Einstein condensate in a double
well potential or on a two-component condensate with inter-state coupling.