Quantum effects on curve crossing in a Bose-Einstein condensate

Formation of atomic pairs by the dissociation of a molecular condensate or by inelastic collisions in an atomic condensate due to a time-dependent curve crossing process is studied beyond the mean-field approximation. The number of atoms formed by the spontaneous process is described by a Landau-Zener formula multiplied by an exponential amplification factor due to quantum many-body effects. The atomic pairs are formed in an entangled (squeezed) state. The rate of stimulated processes depends on the relative phase of the two fields.