Arnol'd Tongues and Quantum Accelerator Modes

Abstract

The stable periodic orbits of an area-preserving map on the 2-torus, which is formally a variant of the Standard Map, have been shown to explain the quantum accelerator modes that were discovered in experiments with laser-cooled atoms. We show that their parametric dependence exhibits Arnol'd-like tongues and perform a perturbative analysis of such structures. We thus explain the arithmetical organisation of the accelerator modes and discuss experimental implications thereof.

20 pages, 6 encapsulated postscript figures

References in corpus (5)

• Wannier-Stark resonances in optical and semiconductor superlattices
• Stable Quantum Resonances in Atom Optics
• Experimental observation of high-order quantum accelerator modes
• Anomalous transport and quantum-classical correspondence
• Gravity-Sensitive Quantum Dynamics in Cold Atoms

Cited by in corpus (11)

• Decay of Quantum Accelerator Modes
• Quantum Accelerator Modes from the Farey Tree
• Quantum Resonances and Ratchets in Free-Falling Frames
• Effects of atomic interactions on Quantum Accelerator Modes
• Steering random walks with kicked ultracold atoms
• Quantum Accelerator Modes near Higher-Order Resonances
• Fidelity for kicked atoms with gravity near a quantum resonance
• Classical and Quantum Transport in One-Dimensional Periodically Kicked Systems
• Regimes of stability of accelerator modes
• Rotating Accelerator-Mode Islands
• Spinor Dynamics of Quantum Accelerator Modes near Higher Order Resonances