  We introduce a toy model that allows us to study the physical properties of a
spin impurity coupled to the electrons in the superconducting island. We show
that when the coupling of the spin is of the order of the superconducting gap
two almost degenerate subgap states are formed. By computing the Berry phase
that is associated with the superconducting phase rotations in this model, we
prove that these subgap states are characterized by a different charge and
demonstrate that the switching between these states has the same effect as
quasiparticle poisoning (unpoisoning) of the island. We also show that an
impurity coupled to both the island and the lead generates Josepshon current
fluctuations.
