Radial Squeezed States and Rydberg Wave Packets

We outline an analytical framework for the treatment of radial Rydberg wave packets produced by short laser pulses in the absence of external electric and magnetic fields. Wave packets of this type are localized in the radial coordinates and have p-state angular distributions. We argue that they can be described by a particular analytical class of squeezed states, called radial squeezed states. For hydrogenic Rydberg atoms, we discuss the time evolution of the corresponding hydrogenic radial squeezed states. They are found to undergo decoherence and collapse, followed by fractional and full revivals. We also present their uncertainty product and uncertainty ratio as functions of time. Our results show that hydrogenic radial squeezed states provide a suitable analytical description of hydrogenic Rydberg atoms excited by short-pulsed laser fields.Comment: published in Physical Review

Elliptical Squeezed States and Rydberg Wave Packets

We present a theoretical construction for closest-to-classical wave packets localized in both angular and radial coordinates and moving on a keplerian orbit. The method produces a family of elliptical squeezed states for the planar Coulomb problem that minimize appropriate uncertainty relations in radial and angular coordinates. The time evolution of these states is studied for orbits with different semimajor axes and eccentricities. The elliptical squeezed states may be useful for a description of the motion of Rydberg wave packets excited by short-pulsed lasers in the presence of external fields, which experiments are attempting to produce. We outline an extension of the method to include certain effects of quantum defects appearing in the alkali-metal atoms used in experiments.Comment: published in Phys. Rev. A, vol. 52, p. 2234, Sept. 199

Is Schr\"{o}dinger's Conjecture for the Hydrogen Atom Coherent States Attainable

We construct the most general SO(4,2) hydrogen atom coherent states which are the counterpart of Schr\"{o}dinger's harmonic oscillator coherent states. We show that these states cannot be localized and cannot follow the classical orbits. Thus, Schr\"{o}dinger's conjecture for the hydrogen atom coherent states is unattainable.Comment: 10 pages, report

Keplerian Squeezed States and Rydberg Wave Packets

We construct minimum-uncertainty solutions of the three-dimensional Schr\"odinger equation with a Coulomb potential. These wave packets are localized in radial and angular coordinates and are squeezed states in three dimensions. They move on elliptical keplerian trajectories and are appropriate for the description of the corresponding Rydberg wave packets, the production of which is the focus of current experimental effort. We extend our analysis to incorporate the effects of quantum defects in alkali-metal atoms, which are used in experiments.Comment: accepted for publication in Physical Review

Quantum Defects and the Long-Term Behavior of Radial Rydberg Wave Packets

We show that a theoretical description of radial Rydberg wave packets in alkali-metal atoms based solely on hydrogenic wave functions and energies is insufficient to explain data that could be obtained in pump-probe experiments with current technology. The modifications to long-term revival times induced by quantum defects cannot be obtained by direct scaling of the hydrogenic results. Moreover, the effects of laser detuning and quantum defects are different. An alternative approach providing analytical predictions using supersymmetry-based quantum-defect theory is presented.Comment: IUHET 281, June 1994, to appear in Rapid Communications, Physical Review A (December 1994

Long-Term Evolution and Revival Structure of Rydberg Wave Packets for Hydrogen and Alkali-Metal Atoms

This paper begins with an examination of the revival structure and long-term evolution of Rydberg wave packets for hydrogen. We show that after the initial cycle of collapse and fractional/full revivals, which occurs on the time scale $t_{\rm rev}$, a new sequence of revivals begins. We find that the structure of the new revivals is different from that of the fractional revivals. The new revivals are characterized by periodicities in the motion of the wave packet with periods that are fractions of the revival time scale $t_{\rm rev}$. These long-term periodicities result in the autocorrelation function at times greater than $t_{\rm rev}$ having a self-similar resemblance to its structure for times less than $t_{\rm rev}$. The new sequence of revivals culminates with the formation of a single wave packet that more closely resembles the initial wave packet than does the full revival at time $t_{\rm rev}$, i.e., a superrevival forms. Explicit examples of the superrevival structure for both circular and radial wave packets are given. We then study wave packets in alkali-metal atoms, which are typically used in experiments. The behavior of these packets is affected by the presence of quantum defects that modify the hydrogenic revival time scales and periodicities. Their behavior can be treated analytically using supersymmetry-based quantum-defect theory. We illustrate our results for alkali-metal atoms with explicit examples of the revival structure for radial wave packets in rubidium.Comment: To appear in Physical Review A, vol. 51, June 199

Atomic Supersymmetry, Rydberg Wave Packets, and Radial Squeezed States

We study radial wave packets produced by short-pulsed laser fields acting on Rydberg atoms, using analytical tools from supersymmetry-based quantum-defect theory. We begin with a time-dependent perturbative calculation for alkali-metal atoms, incorporating the atomic-excitation process. This provides insight into the general wave packet behavior and demonstrates agreement with conventional theory. We then obtain an alternative analytical description of a radial wave packet as a member of a particular family of squeezed states, which we call radial squeezed states. By construction, these have close to minimum uncertainty in the radial coordinates during the first pass through the outer apsidal point. The properties of radial squeezed states are investigated, and they are shown to provide a description of certain aspects of Rydberg atoms excited by short-pulsed laser fields. We derive expressions for the time evolution and the autocorrelation of the radial squeezed states, and we study numerically and analytically their behavior in several alkali-metal atoms. Full and fractional revivals are observed. Comparisons show agreement with other theoretical results and with experiment.Comment: published in Physical Review

How do wave packets spread? Time evolution on Ehrenfest time scales

We derive an extension of the standard time dependent WKB theory which can be applied to propagate coherent states and other strongly localised states for long times. It allows in particular to give a uniform description of the transformation from a localised coherent state to a delocalised Lagrangian state which takes place at the Ehrenfest time. The main new ingredient is a metaplectic operator which is used to modify the initial state in a way that standard time dependent WKB can then be applied for the propagation. We give a detailed analysis of the phase space geometry underlying this construction and use this to determine the range of validity of the new method. Several examples are used to illustrate and test the scheme and two applications are discussed: (i) For scattering of a wave packet on a barrier near the critical energy we can derive uniform approximations for the transition from reflection to transmission. (ii) A wave packet propagated along a hyperbolic trajectory becomes a Lagrangian state associated with the unstable manifold at the Ehrenfest time, this is illustrated with the kicked harmonic oscillator.Comment: 30 pages, 3 figure

Edge-Magnetoplasmon Wave-Packet Revivals in the Quantum Hall Effect

The quantum Hall effect is necessarily accompanied by low-energy excitations localized at the edge of a two-dimensional electron system. For the case of electrons interacting via the long-range Coulomb interaction, these excitations are edge magnetoplasmons. We address the time evolution of localized edge-magnetoplasmon wave packets. On short times the wave packets move along the edge with classical E cross B drift. We show that on longer times the wave packets can have properties similar to those of the Rydberg wave packets that are produced in atoms using short-pulsed lasers. In particular, we show that edge-magnetoplasmon wave packets can exhibit periodic revivals in which a dispersed wave packet reassembles into a localized one. We propose the study of edge-magnetoplasmon wave packets as a tool to investigate dynamical properties of integer and fractional quantum-Hall edges. Various scenarios are discussed for preparing the initial wave packet and for detecting it at a later time. We comment on the importance of magnetoplasmon-phonon coupling and on quantum and thermal fluctuations.Comment: 18 pages, RevTex, 7 figures and 2 tables included, Fig. 5 was originally 3Mbyte and had to be bitmapped for submission to archive; in the process it acquired distracting artifacts, to upload the better version, see http://physics.indiana.edu/~uli/publ/projects.htm

Quantum Interference: From Kaons to Neutrinos (with Quantum Beats in between)

Using the vehicle of resolving an apparent paradox, a discussion of quantum interference is presented. The understanding of a number of different physical phenomena can be unified, in this context. These range from the neutral kaon system to massive neutrinos, not to mention quantum beats, Rydberg wave packets, and neutron gravity.Comment: 12 pages, LaTeX, 3 figure