  We study the limitations for entanglement due to collisional decoherence in a
Bose-Einstein condensate. Specifically we consider relative number squeezing
between photons and atoms coupled out from a homogeneous condensate. We study
the decay of excited quasiparticle modes due to collisions, in condensates of
atoms with one or two internal degrees of freedom. The time evolution of these
modes is determined in the linear response approximation to the deviation from
equilibrium. We use Heisenberg-Langevin equations to derive equations of motion
for the densities and higher correlation functions which determine the
squeezing. In this way we can show that decoherence due to quasiparticle
interactions imposes an important limit on the degree of number squeezing which
may be achieved. Our results are also relevant for the determination of
decoherence times in other experiments based on entanglement, e.g. the slowing
and stopping of light in condensed atomic gases using dark states.
