  We study suppression of nonadiabatic transitions during adiabatic generation
of a cat-like state (a superposition of different size cat states) 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-like 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-like state
and a spin squeezed state.
