Observation of Subdiffusive Dynamic Scaling in a Driven and Disordered Bose Gas

We explore the dynamics of a tuneable box -trapped Bose gas under strong periodic forcing in the presence of weak disorder. In absence of interparticle interactions, the interplay of the drive and disorder results in an isotropic nonthermal momentum distribution that shows subdiffusive dynamic scaling, with sublinear energy growth and the universal scaling function captured well by a compressed exponential. We explain that this subdiffusion in momentum space can naturally be understood as a random walk in energy space. We also experimentally show that for increasing interaction strength, the gas behavior smoothly crosses over to wave turbulence characterized by a power -law momentum distribution, which opens new possibilities for systematic studies of the interplay of disorder and interactions in driven quantum systems.