Nondispersive wave packets -- control through chaos

Nondispersive wave packets were predicted to emerge in periodically driven Rydberg atoms a little more than 10 years ago [1], and have now been observed in the laboratory [2]. I shall illustrate how these robust, generic ``quantum particles'' and their relatives naturally emerge from the theory of chaotic quantum systems [3], and thus open new perspectives for robust quantum control in various experimental settings -- from one and two-electron [4] atoms under periodic or impulsive [5] driving to cold atoms in flashing periodic potentials, possibly amended by harmonic confinement [6]. Besides the fundamental underlying (nonlinear) resonance phenomena also some more subtle properties will be discussed, including open questions within the realm of spectral theory. \begin{itemize} \item[1] A. Buchleitner, th\`ese de doctorat, Universit\'e Paris 6 (1993); I. Bialynicki-Birula, M. Kalinski, and J. H. Eberly, Phys. Rev. Lett. {\bf 73}, 1777 (1994); D. Delande and A. Buchleitner, Adv. At. Mol. Opt. Phys. {\bf 34}, 85 (1994). \item[2] H. Maeda and T. F. Gallagher, Phys. Rev. Lett. {\bf 92}, 133004 (2004). \item[3] A. Buchleitner, D. Delande, and J. Zakrzewski, Phys. Rep. {\bf 386}, 409 (2002). \item[4] J. Madro\~nero, PhD thesis, Ludwig-Maximilians-Universit\"at M\"unchen (2004), {\script http://edoc.ub.uni-muenchen.de/archive/00002187}. \item[5] D.G. Arb\'o et al., Phys. Rev. A {\bf 67}, 63401 (2003). \item[6] A.R.R. de Carvalho and A. Buchleitner, Phys. Rev. Lett. {\bf 93}, 204101 (2004). \end{itemize}