Effects of atomic interactions on Quantum Accelerator Modes

We consider the influence of the inclusion of interatomic interactions on the delta-kicked accelerator model. Our analysis concerns in particular quantum accelerator modes, namely quantum ballistic transport near quantal resonances. The atomic interaction is modelled by a Gross-Pitaevskii cubic nonlinearity, and we address both attractive (focusing) and repulsive (defocusing) cases. The most remarkable effect is enhancement or damping of the accelerator modes, depending on the sign of the nonlinear parameter. We provide arguments showing that the effect persists beyond mean-field description, and lies within the experimentally accessible parameter range.Comment: 4 pages, 6 figure

On the Spectrum of the Resonant Quantum Kicked Rotor

It is proven that none of the bands in the quasi-energy spectrum of the Quantum Kicked Rotor is flat at any primitive resonance of any order. Perturbative estimates of bandwidths at small kick strength are established for the case of primitive resonances of prime order. Different bands scale with different powers of the kick strength, due to degeneracies in the spectrum of the free rotor.Comment: Description of related published work has been expanded in the Introductio

What determines the spreading of a wave packet?

The multifractal dimensions D2^mu and D2^psi of the energy spectrum and eigenfunctions, resp., are shown to determine the asymptotic scaling of the width of a spreading wave packet. For systems where the shape of the wave packet is preserved the k-th moment increases as t^(k*beta) with beta=D2^mu/D2^psi, while in general t^(k*beta) is an optimal lower bound. Furthermore, we show that in d dimensions asymptotically in time the center of any wave packet decreases spatially as a power law with exponent D_2^psi - d and present numerical support for these results.Comment: Physical Review Letters to appear, 4 pages postscript with figure

Arnol'd Tongues and Quantum Accelerator Modes

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.Comment: 20 pages, 6 encapsulated postscript figure