Observing the loss and revival of long-range phase coherence through disorder quenches

Relaxation of quantum systems is a central problem in nonequilibrium physics. In contrast to classical systems, the underlying quantum dynamics results not only from atomic interactions but also from the long-range coherence of the many-body wave function. Experimentally, nonequilibrium states of quantum fluids are usually created using moving objects or laser potentials, directly perturbing and detecting the system's density. However the fate of long-range phase coherence for hydrodynamic motion of disordered quantum systems is less explored, especially in three dimension. Here, we unravel how the density and phase coherence of a Bose-Einstein condensate of $^6$Li$_2$ molecules respond upon quenching on or off an optical speckle potential. We find that, as the disorder is switched on, long-range phase coherence breaks down one order of magnitude faster than the density of the quantum gas responds. After removing it, the system needs two orders of magnitude longer times to reestablish quantum coherence, compared to the density response. We compare our results with numerical simulations of the Gross-Pitaevskii equation on large three-dimensional grids, finding an overall good agreement. Our results shed light on the importance of long-range coherence and possibly long-lived phase excitations for the relaxation of nonequilibrium quantum many-body systems.