Quantum Accelerator Modes from the Farey Tree

Abstract

We show that mode-locking finds a purely quantum non-dissipative counterpart in atom-optical quantum accelerator modes. These modes are formed by exposing cold atoms to periodic kicks in the direction of the gravitational field. They are anchored to generalized Arnol'd tongues, parameter regions where driven nonlinear classical systems exhibit mode-locking. A hierarchy for the rational numbers known as the Farey Tree provides an ordering of the Arnol'd tongues and hence of experimentally observed accelerator modes.

Final published version

References in corpus (6)

• Non-dispersive wave packets in periodically driven quantum systems
• Stable Quantum Resonances in Atom Optics
• Experimental observation of high-order quantum accelerator modes
• Web-assisted tunneling in the kicked harmonic oscillator
• Quantum Mechanical Cumulant Dynamics near Stable Periodic Orbits in Phase Space: Application to the classical-like dynamics of quantum accelerator modes
• Arnol'd Tongues and Quantum Accelerator Modes

Cited by in corpus (14)

• Exploring the phase space of the quantum delta kicked accelerator
• Macroscopic Quantum Self-Trapping in Dynamical Tunnelling
• Nonlinear resonances in δ-kicked Bose-Einstein Condensates
• Quantum Resonances and Ratchets in Free-Falling Frames
• The manifestation of quantum resonances and antiresonances in a finite temperature dilute atomic gas
• Quantum resonances in an atom-optical delta-kicked harmonic oscillator
• Pseudo-classical theory for fidelity of nearly resonant quantum rotors
• Power-law behavior in the quantum-resonant evolution of the delta-kicked accelerator
• Quantum Accelerator Modes near Higher-Order Resonances
• Fractional resonances in the atom-optical delta-kicked accelerator
• Classical and Quantum Transport in One-Dimensional Periodically Kicked Systems
• Mechanism of the Resonant Enhancement of Electron Drift in Nanometre Semiconductor Superlattices Subjected to Electric and Inclined Magnetic Fields
• An $\epsilon$-pseudoclassical model for quantum resonances in a cold dilute atomic gas periodically driven by finite-duration standing-wave laser pulses
• Spinor Dynamics of Quantum Accelerator Modes near Higher Order Resonances