  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.
