Proposal of a Cold-atom Realization of Quantum Maps with Hofstadter's Butterfly Spectrum

TL;DR

This paper proposes a cold-atom experimental setup to realize quantum maps exhibiting Hofstadter's butterfly spectrum, linking classical and quantum chaos models and expanding experimental possibilities.

Contribution

It introduces a novel cold-atom realization of quantum maps with Hofstadter's butterfly spectrum, connecting the kicked Harper and kicked rotor models.

Findings

Proposes a feasible cold-atom experimental scheme.

Identifies connections between different chaos models.

Highlights differences from existing models.

Abstract

Quantum systems with Hofstadter's butterfly spectrum are of fundamental interest to many research areas. Based upon slight modifications of existing cold-atom experiments, a cold-atom realization of quantum maps with Hofstadter's butterfly spectrum is proposed. Connections and differences between our realization and the kicked Harper model are identified. This work also exposes, for the first time, a simple connection between the kicked Harper model and the kicked rotor model, the two paradigms of classical and quantum chaos.