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The role of disorder on physical systems has been widely studied in themacroscopic and microscopic world. While static disorder is well understood inmany cases, the impact of time-dependent disorder on quantum gases is stillpoorly investigated. In our experimental setup, we introduce and characterize amethod capable of producing time-controlled optical-speckle disorder.Experimentally, coherent light illuminates a combination of a static and arotating diffuser, thereby collecting a spatially varying phase due to thediffusers' structure and a temporally variable phase due to the relativerotation. Controlling the rotation of the diffuser allows changing the specklerealization or, for future work, the characteristic time scale of the change ofthe speckle pattern, i.e. the correlation time, matching typical time scales ofthe quantum gases investigated. We characterize the speckle pattern ex-situ bymeasuring its intensity distribution cross-correlating different intensitypatterns. In-situ, we observe its impact on a molecular Bose-Einsteincondensate (BEC) and cross-correlate the density distributions of BECs probedin different speckle realizations. As one diffuser rotates relative to theother around the common optical axis, we trace the optical speckle's intensitycross-correlations and the quantum gas' density cross-correlations. Our resultsshow comparable outcomes for both measurement methods. The setup allows us totune the disorder potential adapted to the characteristics of the quantum gas.These studies pave the way for investigating nonequilibrium physics ininteracting quantum gases using controlled dynamical-disorder potentials.

Characterizing quantum gases in time-controlled disorder realizations using cross-correlations of density distributions