Discrete Scaling Laws for Transiently Localized Rydberg States

D. G. ARBÓ; C. O. REINHOLD; J. BURGDÖRFER

Tucson, Arizona (USA)

Congreso; 2004 Division of Atomic, Molecular and Optical Physics Annual Meeting; 2004

Transient phase-space localization of Rydberg wavepackets can be achieved by application of a single short half-cycle pulse to a strongly polarized quasi-one-dimensional Rydberg atom [1].  Phase-space localization results from a focusing effect analogous to rainbow scattering. These essential features remain valid in quantum mechanics and are evident in the Husimi distribution of the wavepacket.  We show that the width in momentum space is a good measure of the degree of localization and that its recurrent minima as a function of time obey a universal scaling rule that is controlled by the effective Planck constant heff of the problem. Maximum focusing is reached in the classical limit (heff << 1). The present results allow the determination of the focusing time for high principal quantum numbers, where quantum calculations are still prohibitively complicated, by rescaling results for lower principal quantum numbers. The break time beyond which classical calculations deviate from quantum predictions can be determined and thus the validity of the classical description of a given experiment can be estimated. The present quantum scaling relates experiments for disparate principal quantum numbers [1,2] where break times differ from each other by around five orders of magnitude.   [1] D.G. Arbó et al, Phys. Rev. A 67, 063401 (2003); C.L. Stokely et al, Phys. Rev. A 67, 013403 (2003). [2] R.R. Jones, Phys. Rev. Lett. 76, 3927 (1996).