Classical and quantum scaling for localization of half-cycle pulse-driven Rydberg wave packets

Abstract

Rydberg wave packets generated by a single half-cycle pulse (HCP) interacting with a stationary Rydberg state periodically localize within a narrow region in both momentum and coordinate space (i.e., phase space). This property is the key to shaping and manipulating wave packets. We investigate the dependence of this transient localization and focusing on the principal quantum number n and on the strength of the ultrashort HCP (``kick strength,'' $\ensuremath{\Delta}p).$ It is shown that the localization in momentum space of the wave packet, quantified by the momentum width, obeys a universal scaling rule which is controlled by an effective Planck constant ${\ensuremath{\Elzxh}}_{\mathrm{eff}}.$ Maximum focusing is reached in the classical limit $({\ensuremath{\Elzxh}}_{\mathrm{eff}}\ensuremath{\rightarrow}0).$