  We study how to efficiently control an interacting few-body system consisting
of three harmonically trapped bosons. Specifically we investigate the process
of modulating the interparticle interactions to drive an initially
non-interacting state to a strongly interacting one, which is an eigenstate of
a chosen Hamiltonian. We also show that for unbalanced subsystems, where one
can individually control the different inter- and intra-species interactions,
complex dynamics originates when the symmetry of the ground state is broken by
phase separation. However, as driving the dynamics too quickly can result in
unwanted excitations of the final state, we optimize the driven processes using
shortcuts to adiabaticity, which are designed to reduce these excitations at
the end of the interaction ramp ensuring that the target eigenstate is reached.

Quantum Gases;Quantum Physics