Subdiffusive dynamic scaling in a chaotic noninteracting Bose gas

Investigating the properties of quantum-chaotic states is of fundamental interest, but experimental realizations of these systems are few (a famous example being the quantum kicked rotor). Here, we realize a three-dimensional quantum-chaotic system by strongly driving a noninteracting Bose-Einstein condensate trapped in a cylindrical box trap with disorder. The full momentum distribution exhibits sub-diffusive dynamic scaling, which we reproduce in Schrödinger equation simulations. The timescale of the dynamics depends on the disorder strength and parameters of the drive, but the shape of momentum-space profiles and their scaling exponents are robust. Finally, we show that increasing the strength of interparticle interactions smoothly connects this single-particle behavior with that of a wave-turbulent cascade.