  In this article we consider a bosonic Josephson junction, a model system
composed by two coupled nonlinear quantum oscillators which can be implemented
in various physical contexts, initially prepared in a product of weakly
populated coherent states. We quantify the maximum achievable entanglement
between the modes of the junction and then use shortcuts to adiabaticity, a
method developed to speed up adiabatic quantum dynamics, as well as numerical
optimization, to find time-dependent controls (the nonlinearity and the
coupling of the junction) which bring the system to a maximally entangled
state.
