Quantum diffusion with disorder, noise and interaction

TL;DR

This paper investigates how disorder, noise, and interactions influence quantum wavepacket diffusion in ultracold atoms, revealing complex anomalous diffusion behaviors and their modeling through a generalized diffusion equation.

Contribution

It demonstrates the combined effects of noise and interaction on quantum diffusion, introducing a generalized diffusion model for complex anomalous behaviors.

Findings

Disorder causes Anderson localization in the system.

Noise and interaction suppress localization and promote transport.

Combined noise and interaction lead to complex anomalous diffusion.

Abstract

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 disordered lattice with controlled noise and tunable interaction. The presence of 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 are 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 regimes of strong interaction or narrowband noise.