  We probe the response of ultracold, interacting Fermi gases of Lithium (Li)
atoms in the BEC-BCS crossover to strong perturbations in space and time via
rapidly switched optical disorder potentials with focus on the BEC side. We
measure the time evolution of long-range phase coherence quantified via the
ability of the gas to expand hydrodynamically. While in the presence of static
disorder, the effects on a Bardeen-Cooper-Schrieffer (BCS) type superfluid are
predicted to be much smaller compared to a molecular Bose-Einstein condensate
(BEC), we find that the quantum properties of a resonantly interacting, unitary
Fermi gas are more strongly suppressed in the presence of quenched disorder
than in a molecular BEC. For quenches from a disordered potential, we find that
the unitary Fermi gas never recovers quantum hydrodynamics for all parameters
studied, while a molecular BEC always recovers quantum hydrodynamics, even when
the quench leads to strong particle losses of up to 70 %. Temperature
measurements indicate an additional heating channel specific to gases close to
resonant interactions, leading to strong local dephasing or pair breaking. Our
work illustrates the striking difference between the nonequilibrium phase
diagram of the time-dependent disordered BEC-BCS crossover compared to that of
the static-disorder case. Moreover, our results suggest an important role of
local dephasing of fermionic pairs by time-dependent local perturbations, which
could be a key contribution to the destruction of macroscopic quantum
properties for time-dependent perturbations.
