Emergent Particle Cascade in a Periodically Driven One-Dimensional Interacting Bose–Hubbard System

Cascade is known as the transfer of conserved quantities across scales through nonlinear mode coupling. Originally studied in classical fluids, it has recently been realized in quantum systems. However, whether a stable cascade can emerge in a strongly interacting quantum system during the driving process remains an open question, where heating competes with the cascade. In this work, we investigate the far-from-equilibrium dynamics of a one-dimensional Bose–Hubbard system at half-filling, driven periodically by a spatially modulated chemical potential that injects energy at a single intermediate wavevector. By performing large-scale simulations, we uncover that the momentum distribution follows a quasi-steady power-law scaling in the region [π/4,π/2]. Notably, this particle cascade in momentum space is stable only under weak driving in the weakly interacting regime against thermalization, while it persists up to substantially larger amplitudes in the strongly interacting regime. Our results reveal an interacting many-body quantum counterpart of periodically driven turbulent wave cascades and indicate a mechanism by which interactions stabilize universal distributions under far-from-equilibrium conditions.