Quantum kicked rotor (QKR) with cold atomic gases and standing optical waves was investigated. It was found that QKR exhibits dynamical localization in the momentum space. The weak-localization regime concentrating on the Ehrenfest time scale was also considered. The results show that the onset of the dynamical localization is essentially delayed by four Ehrenfest times and give quantitative predictions suitable for an experimental verification.
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We would like to thank A. Altland, S. Fishman, J. Liu, and C. Zhang for helpful discussions. C. T. and A. L. are supported by NSF Grant No. DMR-0120702; A. K. was supported by the A. P. Sloan Foundation and NSF Grant No. DMR-0405212.