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Physical Review Letters

Navigating Localized Wave Packets in Phase Space

Wen Kui Zhao, J. J. Mestayer, J. C. Lancaster, F. B. Dunning, Carlos O Reinhold, S. Yoshida, Joachim Burgdörfer

Published Dec 20, 2006• 16 citations
Publisher

Abstract

The ability to localize and to steer Rydberg wave packets in phase space using tailored sequences of half-cycle pulses is demonstrated. Classical phase-space portraits are used to explain the method and to illustrate the level of control that can be achieved. This is confirmed experimentally by positioning a phase-space-localized wave packet at the center of a stable island or navigating it around its periphery. This work provides a valuable starting point for further engineering of electronic wave functions.

DOI
10.1103/physrevlett.97.253003

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•Jan 1, 2009•0 citations
The ability to localize and to steer Rydberg wave packets in phase space using tailored sequences of half-cycle pulses is demonstrated. Classical phase-space portraits are used to explain the method and to illustrate the level of control that can be achieved. This is confirmed experimentally by positioning a phase-space-localized wave packet at the center of a stable island or navigating it around its periphery. This work provides a valuable starting point for further engineering of electronic wave functions.
We present protocols for steering a Rydberg wave packet towards a preferred region in phase space using a train of half-cycle pulses. Developing such protocols is aided by classical phase space portraits. The classical phase space changes its structure as the frequency and the strength of a train of pulses are modulated. The quantum wave packet can be made to follow such a change. The movement of the wave packet can thus be controlled by a proper modulation of the perturbation. In addition, this technique can be used to create a focused wave packet or to transfer it from one island to another associated with a different quasi-periodic motion.
A technique for generating Rydberg wavepackets in preferred target states is demonstrated that exploits the mixed phase space structure of the periodically `kicked' Rydberg atom. Experimental data and classical simulations for very-high- n Rydberg atoms are presented that show that application of a train of equispaced, unidirectional half-cycle pulses can lead to localization of the final wavepacket in classical stable islands. The product wavepackets are examined using a delayed half-cycle probe pulse. It is demonstrated that the motion of the wavepackets is either quasiperiodic or random depending on whether or not the initial state of the atom overlaps a stable island.
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 $({\ensuremath{\Elzxh}}_{\mathrm{eff}}\ensuremath{\rightarrow}0).$
Atoms in high-lying Rydberg states with large values of principal quantum number n, n ≥300, form a valuable laboratory in which to explore the control and manipulation of quantum states of mesoscopic size using carefully tailored sequences of short electric field pulses whose characteristic times (duration and/or rise/fall times) are less than the classical electron orbital period. Atoms react to such pulse sequences very differently than to short laser or microwave pulses providing the foundation for a number of new approaches to engineering atomic wavefunctions. The remarkable level of control that can be achieved is illustrated with reference to the generation of localized wavepackets in Bohr-like near-circular orbits, and the production of non-dispersive wavepackets under periodic driving and their transport to targeted regions of phase space. New protocols continue to be developed that will allow even tighter control with the promise of new insights into quantum-classical correspondence, information storage in mesoscopic systems, physics in the ultra-fast ultra-intense regime, and non-linear dynamics in driven systems.