Unraveling the role of long-range coherence for superfluid dynamics by disorder quenches

We investigate the density and superfluid-expansion response of an interacting molecular Bose-Einstein condensate of $^6$Li atoms upon quenches of a laser speckle pattern. We track the response times on which the system relaxes to a new equilibrium and relate the time scales to fundamental energy scales of the system. We find that the density responds on a time scale which is compatible with both superfluid and classical transport. By contrast, superfluid expansion breaks down an order of magnitude faster than the corresponding density response, which we can relate to phase gradients imprinted on the system destroying superfluid expansion. Further, the time scale on which the system relaxes from a quench out of disorder to superfluid expansion is two orders of magnitude longer than the corresponding density time scale. This suggests complex phase patterns relaxing on long time scales before superfluid expansion is reestablished. Our results shed light onto the importance of long-range phase coherence for superfluid flow, and also suggest a possible route of studying complex phase dynamics in superfluids by imprinting disordered phases.