Chaotic quantum ratchets and filters with cold atoms in optical lattices: Analysis using Floquet states

Recently, cesium atoms in optical lattices subjected to cycles of unequally spaced pulses have been found to show interesting behavior: they represent an 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 δ-kicked rotor (δ-QKR). We investigate here the properties of the corresponding eigenstates (Floquet states) in the parameter regime of the recent experiments and compare them with those of the eigenstates of the δ-QKR at similar kicking strengths. We show that by studying 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.