^{1}, C. O. Reinhold

^{2}, S. Yoshida

^{3}and J. Burgdörfer

^{4}

### Abstract

We describe how, almost 100 years after the introduction of the Bohr model of the atom, it is now possible using pulsed electric fields to create localized wavepackets in high Rydberg atoms that travel in near-circular Bohr-like orbits mimicking the behavior of a classical electron. The protocols employed are explained with the aid of quantum and classical dynamics. Although many aspects of the underlying behavior can be described using classical arguments, purely quantum effects such as revivals can be seen even for .

The work by the authors and their colleagues on which this article is based was supported by NSF under Grant No. 0560732, the Robert A. Welch Foundation under Grant No. C-0734, the Office of Basic Energy Sciences, U.S. Department of Energy, through Contract No. AC05-00OR22725 to Oak Ridge National Laboratory managed by UT-Batelle LLC, and the Austrian Science Fund under Grant No. SFB016. The authors are indebted to B. Wyker for help in preparing the figures.

I. INTRODUCTION

II. WAVEPACKETS

III. PRODUCTION AND CHARACTERIZATION OF CIRCULAR WAVEPACKETS

IV. TRANSIENT LOCALIZATION OF CIRCULAR STATES

V. NONDISPERSIVE WAVEPACKETS

VI. SUMMARY

### Key Topics

- Monte Carlo methods
- 9.0
- Angular momentum
- 8.0
- Electric fields
- 8.0
- Probability theory
- 7.0
- Rydberg states
- 6.0

## Figures

Azimuthal localization resulting from superposition of three plane waves with , 15, and 16. (a) The real parts of these functions (that is, cosine functions) and (b) the square of their sum. (c) The corresponding azimuthal probability density .

Azimuthal localization resulting from superposition of three plane waves with , 15, and 16. (a) The real parts of these functions (that is, cosine functions) and (b) the square of their sum. (c) The corresponding azimuthal probability density .

Time evolution of the probability density associated with the ideal Bohr wavepacket, Eq. (3), for and . The line denotes a circular trajectory. The axes are labeled in scaled units (see text).

Time evolution of the probability density associated with the ideal Bohr wavepacket, Eq. (3), for and . The line denotes a circular trajectory. The axes are labeled in scaled units (see text).

Schematic of the time-dependent electric fields applied along the and axes, used to create (and maintain) near-circular states. Snapshots of the electron probability density (projected on the plane) at the times indicated by the arrows are included. The axes are labeled in scaled units.

Schematic of the time-dependent electric fields applied along the and axes, used to create (and maintain) near-circular states. Snapshots of the electron probability density (projected on the plane) at the times indicated by the arrows are included. The axes are labeled in scaled units.

(a) Evolution of the classical trajectory of an electron initially in a highly elliptical orbit oriented along the axis following sudden application of a dc pump field along the axis. (b) Calculated evolution of the distribution of the component of the angular momentum, , for a quasi-1D state initially oriented along the axis.

(a) Evolution of the classical trajectory of an electron initially in a highly elliptical orbit oriented along the axis following sudden application of a dc pump field along the axis. (b) Calculated evolution of the distribution of the component of the angular momentum, , for a quasi-1D state initially oriented along the axis.

Time dependence of the angular probability density distribution of the wavepacket following the turn-off of a pump field of 22 ns duration applied to quasi-1D atoms. To emphasize the effects of azimuthal focusing the distributions are plotted in a frame rotating at . Snapshots of the electron probability density (projected on the plane) at the times indicated are also included.

Time dependence of the angular probability density distribution of the wavepacket following the turn-off of a pump field of 22 ns duration applied to quasi-1D atoms. To emphasize the effects of azimuthal focusing the distributions are plotted in a frame rotating at . Snapshots of the electron probability density (projected on the plane) at the times indicated are also included.

(a) Time dependence of the survival probabilities measured for quasi-1D atoms following the turn-off of a pump field of 44 ns duration using 6 ns long probe pulses directed along the and axes. The lines represent the results of classical trajectory Monte Carlo simulations. (b) Same as for (a) using a probe half-cycle pulse directed along the axis delivering a scaled impulse .

(a) Time dependence of the survival probabilities measured for quasi-1D atoms following the turn-off of a pump field of 44 ns duration using 6 ns long probe pulses directed along the and axes. The lines represent the results of classical trajectory Monte Carlo simulations. (b) Same as for (a) using a probe half-cycle pulse directed along the axis delivering a scaled impulse .

(a) Survival probabilities measured for subject to a pump field of 86 ns duration as a function of time after the turn-off of the pump field using a 6 ns probe pulse directed along the axis. The top insets show snapshots of the electron probability density at the times indicated. (b) Results of quantized classical trajectory Monte Carlo simulations. The middle inset shows the frequency spectrum calculated from the Fourier transform of the experimental and theoretical results. The frequencies are labeled in terms of the corresponding values of .

(a) Survival probabilities measured for subject to a pump field of 86 ns duration as a function of time after the turn-off of the pump field using a 6 ns probe pulse directed along the axis. The top insets show snapshots of the electron probability density at the times indicated. (b) Results of quantized classical trajectory Monte Carlo simulations. The middle inset shows the frequency spectrum calculated from the Fourier transform of the experimental and theoretical results. The frequencies are labeled in terms of the corresponding values of .

Survival probabilities measured as a function of time after the turn-off of a 44 ns long pump field applied to parent quasi-1D atoms. The results are obtained with (a) no half-cycle pulse train applied; (b) and (c) a periodic sequence of half-cycle pulses of strength and period of ≈4.3 ns initiated, together with an offset field (see text), following a 27.5 ns delay. A 6 ns probe pulse was employed. The dots are experimental results, and the lines are the predictions of the classical trajectory Monte Carlo simulations. The inset illustrates the stabilization mechanism (see text).

Survival probabilities measured as a function of time after the turn-off of a 44 ns long pump field applied to parent quasi-1D atoms. The results are obtained with (a) no half-cycle pulse train applied; (b) and (c) a periodic sequence of half-cycle pulses of strength and period of ≈4.3 ns initiated, together with an offset field (see text), following a 27.5 ns delay. A 6 ns probe pulse was employed. The dots are experimental results, and the lines are the predictions of the classical trajectory Monte Carlo simulations. The inset illustrates the stabilization mechanism (see text).

Calculated time-dependent behavior of the electron wavepacket for the conditions in Fig. 8 after ≈100 orbits. The snapshots are taken at (a) 440, (b) 441, (c) 442, and (d) 443 ns after turn-off of the pump field.

Calculated time-dependent behavior of the electron wavepacket for the conditions in Fig. 8 after ≈100 orbits. The snapshots are taken at (a) 440, (b) 441, (c) 442, and (d) 443 ns after turn-off of the pump field.

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