  We derive a model to describe decoherence of atomic clouds in atom-chip traps
taking the excited states of the trapping potential into account. We use this
model to investigate decoherence for a single trapping well and for a pair of
trapping wells that form the two arms of an atom interferometer. Including the
discrete spectrum of the trapping potential gives rise to a decoherence
mechanism with a decoherence rate $\Gamma$ that scales like $\Gamma \sim
1/r_0^4$ with the distance $r_0$ from the trap minimum to the wire.
