Quantum diffusion with disorder, noise and interaction

Disorder, noise and interaction play a crucial role in the transport properties of real systems, but they are typically hard to control and study, both theoretically and experimentally, especially in the quantum case. Here, we explore a paradigmatic problem, the diffusion of a wavepacket, by employing ultra-cold atoms in a quasi-periodic lattice with controlled noise and tunable interaction. The presence of quasi-disorder leads to Anderson localization, while both interaction and noise tend to suppress localization and restore transport, although with completely different mechanisms. When only noise or interaction is present, we observe a diffusion dynamics that can be explained by existing microscopic models. When noise and interaction are combined, we observe instead a complex anomalous diffusion. By combining experimental measurements with numerical simulations, we show that such anomalous behavior can be modeled with a generalized diffusion equation in which the noise- and interaction-induced diffusions enter in an additive manner. Our study reveals also a more complex interplay between the two diffusion mechanisms in the regimes of strong interaction or narrowband noise.