Condensate soliton collisions beyond mean-field theory

Bright solitons in a Bose-Einstein condensate contain thousands of identical atoms held together despite their only weakly attractive contact interactions. Solitons nonetheless behave like a compound object, staying whole in collisions. The effective potential governing their collisions is however strongly affected by inter-soliton quantum coherence in the many-body wave function. We show that separate solitons decohere due to phase diffusion, dependent on their effective ambient temperature, after which their initial mean-field relative phases are no longer well defined or relevant for collisions. In this situation, collisions which occur predominantly repulsive can no longer be described within mean field theory. When considering the time-scales involved in recent soliton experiments where non-equilibrium phenomena play an important role, these features can consistently explain the predominantly repulsive collision dynamics observed in most condensate soliton train experiments.