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Physical Review Letters

Dynamical Stabilization of the Periodically Kicked Rydberg Atom

Carlos O Reinhold, Joachim Burgdörfer, M. T. Frey, F. B. Dunning

Published Dec 29, 1997• 49 citations
Publisher

Abstract

Measurements in which $K(\mathrm{np})$ Rydberg atoms with $n\ensuremath{\sim}388$ are subject to a train of up to 50 half-cycle pulses are reported and reveal a peak in the atomic survival probability for pulse repetition frequencies near the classical orbital frequency. Classical calculations show that this behavior is associated with dynamical stabilization and the periodic orbits in phase space around which stable islands form are identified. This work provides the first direct evidence for dynamical stabilization of a periodically kicked Rydberg atom.

DOI
10.1103/physrevlett.79.5226

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Measurements in which K(np)K(\mathrm{np})K(np) Rydberg atoms with n\ensuremath∼388n\ensuremath{\sim}388n\ensuremath∼388 are subject to a train of up to 50 half-cycle pulses are reported and reveal a peak in the atomic survival probability for pulse repetition frequencies near the classical orbital frequency. Classical calculations show that this behavior is associated with dynamical stabilization and the periodic orbits in phase space around which stable islands form are identified. This work provides the first direct evidence for dynamical stabilization of a periodically kicked Rydberg atom.
We analyze the quantum dynamics of the one-dimensional periodically kicked Rydberg atom. The time-dependent Schr\"odinger equation is solved by employing a nonunitary representation of the period-one evolution operator in a finite basis set that accounts for the outbound probability flux. We find a direct correspondence between stable classical islands in phase space and the quantum Husimi distributions of stable Floquet states. These results explain the pronounced peak recently found experimentally in the frequency-dependent survival probability of Rydberg states subject to a sequence of half-cycle pulses.
The response of quasi-one-dimensional very-high-nnn Rydberg atoms to a periodic train of short unidirectional electric-field pulses, termed half-cycle pulses (HCPs), is studied at high scaled frequencies. Pronounced nonmonotonic structure in the survival probability is observed as NNN, the number of HCPs in the train is increased, the survival probability actually increasing with NNN over certain ranges of NNN. This behavior is very sensitive to the polarization of the Rydberg states and is explained with the aid of classical simulations.
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.
The characteristics of strongly-polarized quasi-one-dimensional (quasi-1D) Rydberg atoms produced by photoexcitation of selected Stark states in the n = 350 Stark manifold are investigated by studying their ionization when subject to sub-nanosecond unidirectional electric field pulses, termed half-cycle pulses (HCPs), directed both parallel and perpendicular to the atomic axis. The observed differences in the ionization characteristics provide a measure of the anisotropy of the momentum distribution and thus of the quasi-1D nature of the states. The response of such states to a train of HCPs directed parallel and anti-parallel to the axis of polarization of the initial state is also investigated. Pronounced differences in the survival probability are observed confirming theoretical predictions that the dynamical response of the system will be very different for these two conditions. The presence of noise is also observed to play a crucial role in the dynamics. Reasonable agreement between experiment and theory is achieved.
The influence of a superposed offset field on the response of highly polarized (quasi-1D) very-high-nnn Rydberg atoms to a periodic train of unidirectional half-cycle pulses (HCPs) is investigated, both experimentally and theoretically. It is observed that the presence of an offset field strongly influences the dynamics. The electronic states become transiently stabilized and trapped near the ionization threshold when the net average field they experience is near zero irrespective of whether the HCPs, applied parallel to the atomic axis, are directed towards or away from the nucleus. The nature of this stabilization is explored using Poincar\'e surfaces of section. In large offset fields, direct field ionization becomes possible but it is demonstrated that this can be suppressed by application of an oppositely directed HCP train. The use of such ``frustrated field ionization'' to measure the polarization of Rydberg atoms is discussed.
We demonstrate the use of a periodic train of half-cycle pulses to maintain strongly-localized wave packets in very-high-nnn $(n\ensuremath{\sim}300)$ Rydberg atoms that travel in near-circular orbits about the nucleus. This motion can be followed for hundreds of orbital periods and mimics the original Bohr model of the hydrogen atom which envisioned an electron in circular classical orbit about the nucleus.