  We study how matter-wave interferometry with Bose-Einstein condensates is
affected by hypothetical collapse models and by environmental decoherence
processes. Motivated by recent atom fountain experiments with macroscopic arm
separations, we focus on the observable signatures of first-order and
higher-order coherence for different two-mode superposition states, and on
their scaling with particle number. This can be used not only to assess the
impact of environmental decoherence on many-body coherence, but also to
quantify the extent to which macrorealistic collapse models are ruled out by
such experiments. We find that interference fringes of phase-coherently split
condensates are most strongly affected by decoherence, whereas the quantum
signatures of independent interfering condensates are more immune against
macrorealistic collapse. A many-body enhanced decoherence effect beyond the
level of a single atom can be probed if higher-order correlations are resolved
in the interferogram.
