Chaotic quantum ratchets and filters with cold atoms in optical lattices: properties of Floquet states

Abstract

Recently, cesium atoms in optical lattices subjected to cycles of unequally-spaced pulses have been found to show interesting behavior: they represent the first experimental demonstration of a Hamiltonian ratchet mechanism, and they show strong variability of the Dynamical Localization lengths as a function of initial momentum. The behavior differs qualitatively from corresponding atomic systems pulsed with equal periods, which are a textbook implementation of a well-studied quantum chaos paradigm, the quantum delta-kicked particle (delta-QKP). We investigate here the properties of the corresponding eigenstates (Floquet states) in the parameter regime of the new experiments and compare them with those of the eigenstates of the delta-QKP at similar kicking strengths. We show that, with the properties of the Floquet states, we can shed light on the form of the observed ratchet current as well as variations in the Dynamical Localization length.

arXiv comment9 pages, 9 figures

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• Directed current due to broken time-space symmetry
• Classical and Quantum Hamiltonian Ratchets
• Experimental evidence of dynamical localization and delocalization in a quasi-periodic driven system
• Atoms in double-delta-kicked periodic potentials: chaos with long-range correlations
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• Quantum Ratchets for Quantum Communication with Optical Superlattices
• Chaotic ratchet dynamics with cold atoms in a pair of pulsed optical lattices
• Coherent ratchets in driven Bose-Einstein condensates
• Quantum Resonances and Ratchets in Free-Falling Frames
• Theory of 2$\delta$-kicked Quantum Rotors
• Perturbative analysis of coherent quantum ratchets in cold atom systems
• Directed deterministic classical transport: symmetry breaking and beyond
• Classical diffusion in double-delta-kicked particles
• Statistical Approach to Quantum Chaotic Ratchets
• Weak-Chaos Ratchet Accelerator
• Robust Dynamical Recurrences Based on Floquet Spectrum
• Classical and Quantum Transport in One-Dimensional Periodically Kicked Systems
• Quantum Properties of Double Kicked Systems with Classical Translational Invariance in Momentum