  Using the time-dependent density matrix renormalization group (TDMRG) we
theoretically study the collision of a one-dimensional gas of interacting
bosons with an impurity trapped in a shallow box potential. We study the
dynamic response of both the impurity and the bosonic gas and find an
approximate independence of the sign of the interaction (attractive or
repulsive) between the impurity and the bosons. This sign-independence breaks
down when the interaction energy is of the same order as the box potential
depth, leading to resonant pair tunneling. Our predictions can be tested using
contemporary techniques with ultracold atoms.
