Anomalous Diffusion in a Dynamical Optical Lattice

TL;DR

This paper investigates how atoms in a dynamical optical lattice exhibit tunable anomalous diffusion due to quantum effects, providing insights into localization phenomena in atom-photon systems.

Contribution

It introduces a dynamical Aubry-André model for atom-cavity systems and analyzes the resulting anomalous diffusion behavior.

Findings

Atomic wavepackets show tunable super- and sub-diffusive spreading.

Anomalous diffusion results from interplay between localization and cavity quantum fluctuations.

The model connects quantum localization with dynamical lattice effects.

Abstract

Motivated by experimental progress in strongly coupled atom-photon systems in optical cavities, we study theoretically the quantum dynamics of atoms coupled to a one-dimensional dynamical optical lattice. The dynamical lattice is chosen to have a period that is incommensurate with that of an underlying static lattice, leading to a dynamical version of the Aubry-Andr\'e model which can cause localization of single-particle wavefunctions. We show that atomic wavepackets in this dynamical lattice generically spread via anomalous diffusion, which can be tuned between super-diffusive and sub-diffusive regimes. This anomalous diffusion arises from an interplay between quantum localization and quantum fluctuations of the cavity field.