  We study the dynamics of a one-dimensional system composed of a bosonic
background and one impurity in single- and double-well trapping geometries. In
the limit of strong interactions, this system can be modeled by a spin chain
where the exchange coefficients are determined by the geometry of the trap. We
observe non-trivial dynamics when the repulsion between the impurity and the
background is dominant. In this regime, the system exhibits oscillations that
resemble the dynamics of a Josephson junction. Furthermore, the double-well
geometry allows for an enhancement in the tunneling as compared to the
single-well case.
