Quantum Control of Ultra-cold Atoms: Uncovering a Novel Connection between Two Paradigms of Quantum Nonlinear Dynamics

TL;DR

This paper demonstrates a novel method to control ultra-cold atoms using optical lattices, establishing a connection between two quantum nonlinear dynamics models and enabling experimental realization of Hofstadter's butterfly spectrum.

Contribution

It introduces a new approach linking the kicked rotor and kicked Harper models via tailored optical lattice sequences, facilitating experimental exploration of complex quantum spectra.

Findings

Connection between kicked rotor and kicked Harper models established

Experimental feasibility of realizing Hofstadter's butterfly spectrum shown

Effective Planck constant tunable through control field timing

Abstract

Controlling the translational motion of cold atoms using optical lattice potentials is of both theoretical and experimental interest. By designing two on-resonance time sequences of kicking optical lattice potentials, a novel connection between two paradigms of nonlinear mapping systems, i.e., the kicked rotor model and the kicked Harper model, is established. In particular, it is shown that Hofstadter's butterfly quasi-energy spectrum in periodically driven quantum systems may soon be realized experimentally, with the effective Planck constant tunable by varying the time delay between two sequences of control fields. Extensions of this study are also discussed. The results are intended to open up a new generation of cold-atom experiments of quantum nonlinear dynamics