Formation of matter-wave soliton trains by modulational instabillity

Matter-wave soliton trains were initially observed following an interaction quench in a condensate of ${^{7}\mathrm{Li}}$ atoms\footnote{K.E. Strecker, G.B. Partridge, A. G. Truscott, \& R. G. Hulet, Nature 417, 150 (2002).}. The solitons in the train were observed to interact repulsively, an indication of a phase difference of $\pi$ between neighboring solitons. Although the formation of soliton trains can be understood as resulting from a modulational instability, an explanation for the observed phase-structure remains elusive. We study the formation of soliton trains by characterizing modulational instability across a wide range of scattering lengths. We find universal scaling laws for the number of solitons created by the quench and for the decay in atom number. Through minimally-destructive imaging, we observe real-time dynamics, and show that soliton trains are created with an alternating phase structure, rather than evolving into one.