  We consider the degradation of the dynamics of a Gaussian wave packet in a
harmonic oscillator under the presence of an environment. This last is given by
a single non-degenerate two level system. We analyze how the binary degree of
freedom perturbs the free evolution of the wave packet producing decoherence,
which is quantified by the Loschmidt Echo. This magnitude measures the
reversibility of a perturbed quantum evolution. In particular, we use it here
to study the relative "fragility" of coherent superpositions (cat states) with
respect to incoherent ones. This fragility or sensitivity turns to increase
exponentially with the energy separation of the two components of the
superposition.
