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

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

submitted to the special issue of "Quantum Control of Matter and Light", Journal of Modern Optics

References in corpus (6)

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Cited by in corpus (18)

• Topological Effects in Chiral Symmetric Driven Systems
• Floquet topological phases in a spin-1/2 double kicked rotor
• Recipe for creating an arbitrary number of Floquet chiral edge states
• Non-Hermitian Floquet topological phases in the double-kicked rotor
• Kicked-Harper model vs On-Resonance Double Kicked Rotor Model: From Spectral Difference to Topological Equivalence
• Floquet Hofstadter Butterfly on the Kagome and Triangular Lattices
• Long-lasting Exponential Spreading in Periodically Driven Quantum Systems
• Butterfly Floquet Spectrum in Driven SU(2) Systems
• Generating a Fractal Butterfly Floquet Spectrum in a Class of Driven SU(2) Systems: Eigenstate Statistics
• Chiral limits and effect of light on the Hofstadter butterfly in twisted bilayer graphene
• Exponential Quantum Spreading in a Class of Kicked Rotor Systems near High-Order Resonances
• Generating a Fractal Butterfly Floquet Spectrum in a Class of Driven SU(2) Systems
• Classical and Quantum Transport in One-Dimensional Periodically Kicked Systems
• Floquet engineering the Hofstadter butterfly in the square lattice and its effective Hamiltonian
• Floquet Hofstadter butterfly in trilayer graphene with a twisted top layer
• Statistical properties of power-law random banded unitary matrices in the delocalization-localization transition regime
• Many topological regions on the Bloch sphere of the spin-1/2 double kicked top
• Quantum Properties of Double Kicked Systems with Classical Translational Invariance in Momentum