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We study the limitations for entanglement due to collisional decoherence in aBose-Einstein condensate. Specifically we consider relative number squeezingbetween photons and atoms coupled out from a homogeneous condensate. We studythe decay of excited quasiparticle modes due to collisions, in condensates ofatoms with one or two internal degrees of freedom. The time evolution of thesemodes is determined in the linear response approximation to the deviation fromequilibrium. We use Heisenberg-Langevin equations to derive equations of motionfor the densities and higher correlation functions which determine thesqueezing. In this way we can show that decoherence due to quasiparticleinteractions imposes an important limit on the degree of number squeezing whichmay be achieved. Our results are also relevant for the determination ofdecoherence times in other experiments based on entanglement, e.g. the slowingand stopping of light in condensed atomic gases using dark states.Comment: 16 pages RevTeX, 3 figure

Limitations of squeezing due to collisional decoherence in Bose-Einstein condensates