Exploring Rarefaction Flow in Bose-Einstein Condensates: Dynamics, Riemann Invariants, and Beyond

Bose-Einstein condensates (BECs) offer a remarkable platform for exploring complex quantum flows, revealing intricate dynamics characteristic of superfluids. Among the many fascinating flow phenomena observed in BECs, vortices, vortex rings, and solitons stand out, showcasing the rich landscape of excitations possible within these systems. This work focuses on an especially intriguing flow: rarefaction flow, defined as the expansion of a BEC into a vacuum region. We conduct our study using a BEC in an effectively one-dimensional (1D) channel, an environment that permits a highly controlled examination of this nontrivial flow. Prior studies have established the expansion speed and characteristic parabolic density profile of the rarefaction front, forming a basis for deeper investigation. In this study, we provide a comprehensive characterization of the flow, which includes measurements of Riemann invariants to further elucidate the nature of rarefaction waves in this quantum system. We also present extensions of this work, highlighting potential applications and new directions in the study of BEC dynamics in confined geometries.