Fast and optimal generation of entanglement in bosonic Josephson junctions

We use an exact quantum phase model to study the dynamical generation of particle-entanglement in a bosonic Josephson junction composed by two coupled and interacting Bose-Einstein condensates. Using analytical arguments, we show that linear coupling can accelerate the creation of entanglement with respect to the well known one-axis twisting model where coupling is absent. Furthermore, with a numerical analysis of optimal control schemes, we identify the optimal parameters for the fast generation of metrologically useful entanglement on short time scales: the optimal evolution is generated for a specific ratio between the coupling and the interaction strength.