Measurement of the Second Riemann Invariant in a Rarefied Bose-Einstein condensate

Dilute-gas Bose-Einstein condensates offer a versatile platform for investigating and understanding quantum hydrodynamics phenomena, serving as a valuable benchmark for classical hydrodynamics. This study explores the degenerate dam-break Riemann problem in a channel-constrained superfluid, analogous to behavior exhibited in shallow water waves and non-linear optics systems. While these systems hold similar macroscopic behavior, solutions to the Riemann problem hold different invariants in the classical vs degenerate case. Through the implementation of a quenched pulse in a rarefied population of ultracold atoms, we measure spatially-resolved flow velocity and ascertain the value of the second Riemann invariant. Comparative analysis between numerical simulations and experimental findings validates the theory of degenerate second rarefaction wave behavior.