Suppressing nonadiabatic transitions during adiabatic generation of highly entangled states in bosonic Josephson junctions

We study suppression of nonadiabatic transitions during adiabatic generation of a cat state and a spin squeezed state in a bosonic Josephson junction. In order to minimize the adiabatic error, we use quantum adiabatic brachistochrone, which enables us to track a geometrically efficient path in parameter space under given conditions without requiring additional terms. For creation of a cat state, divergence of the quantum geometric tensor associated with gap closing at the critical point is avoided because of the parity conservation. The resulting schedules of parameters are smooth and monotonically decreasing curves. Use of these schedules offers reduction of time to generate both of a cat state and a spin squeezed state.