Dynamical Critical Behavior of an Attractive Bose-Einstein Condensate Phase Transition

When matter undergoes a continuous phase transition on a finite timescale, the Kibble-Zurek mechanism predicts universal scaling behavior with respect to structure formation. The scaling is dependent on the universality class and is irrelevant to the details of the system. Here, we examine this phenomenon by controlling the timescale of the phase transition to a Bose-Einstein condensate using sympathetic cooling of an ultracold Bose thermal cloud with tunable interactions in an elongated trap. The phase transition results in a diverse number of bright solitons and gray solitons in the condensate that undergo attractive and repulsive interactions, respectively. The power law dependence of the average soliton number on the timescale of the phase transition is measured for each interaction and compared. The results support the Kibble-Zurek mechanism, in that the scaling behavior is determined by universality and does not rely on the interaction properties.