  The model of continuous spontaneous localization (CSL) is the most prominent
consistent modification of quantum mechanics predicting an objective
quantum-to-classical transition. Here we show that precision interferometry
with Bose-Einstein condensed atoms can serve to lower the current empirical
bound on the localization rate parameter by several orders of magnitude. This
works by focusing on the atom count distributions rather than just mean
population imbalances in the interferometric signal of squeezed BECs, without
the need for highly entangled GHZ-like states. In fact, the interplay between
CSL-induced diffusion and dispersive atom-atom interactions results in an
amplified sensitivity of the condensate to CSL. We discuss experimentally
realistic measurement schemes utilizing state-of-the-art experimental
techniques to test new regions of parameter space and, pushed to the limit, to
probe and potentially rule out large relevant parameter regimes of CSL.
