  We examine the time evolution of cold atoms (impurities) interacting with an
environment consisting of a degenerate bosonic quantum gas. The impurity atoms
differ from the environment atoms, being of a different species. This allows
one to superimpose two independent trapping potentials, each being effective
only on one atomic kind, while transparent to the other. When the environment
is homogeneous and the impurities are confined in a potential consisting of a
set of double wells, the system can be described in terms of an effective
spin-boson model, where the occupation of the left or right well of each site
represents the two (pseudo)-spin states. The irreversible dynamics of such
system is here studied exactly, i.e., not in terms of a Markovian master
equation. The dynamics of one and two impurities is remarkably different in
respect of the standard decoherence of the spin - boson system. In particular
we show: i) the appearance of coherence oscillations, i) the presence of super
and sub decoherent states which differ from the standard ones of the spin boson
model, and iii) the persistence of coherence in the system at long times. We
show that this behaviour is due to the fact that the pseudospins have an
internal spatial structure. We argue that collective decoherence also prompts
information about the correlation length of the environment. In a one
dimensional configuration one can change even stronger the qualitative
behaviour of the dephasing just by tuning the interaction of the bath.
