J. Wals

THE ROLE OF THE QUANTUM-DEFECT AND OF HIGH-ORDER DISPERSION IN RYDBERG WAVE-PACKETS

Experimental and theoretical recurrence spectra of Rydberg electron wave packets are presented. Fractional revivals up to the seventh order are observed. In addition we observe a new interference effect: a forerunner wave packet in the first full revival, due to second-order dispersion. Also it is shown that the quantum defect of rubidium shifts the peaks in the interference pattern by the quantum defect modulo one times the classical orbiting period, while it leaves the envelope of the recurrence spectrum unaffected. All these quantum mechanical effects are explained by a Taylor expansion of the phase factors of the stationary states of which the wave packet is composed.

Rydberg electron dynamics in external fields

We review the role which classical trajectories play in quantum-mechanical systems in a more or less chronological order guided by experimental observations. The onset of a renewed interest in classical dynamics was catalysed by the observation of unknown features in the absorption spectra of atoms in the presence of external magnetic and electric fields. Although the most dominant features in these spectra can be accounted for by the simple quantisation conditions for classical electrons, the finer details require a more sophisticated approach. Starting from the Feynman path-integral formalism, Gutzwiller’s periodic-orbit theory is introduced, which is then transformed into the closed-orbit theory developed by Delos et al. Applying this semiclassical theory enabled atomic physicists to understand complicated quantum spectra as a coherent sum of classical trajectories. Newly observed features such as core-scattered orbits and ghost orbits, necessitated adjustments to the standard closed-orbit theory in order to be able to reproduce these new features. Recent results from both scaled-energy experiments and wave-packet experiments are presented to demonstrate the classical dynamics underlying the quantum system as it is currently understood.

Determination of bifurcations from recurrence peaks of electronic wavepackets in an electric field

A new and simple way to determine the bifurcations of electron orbits in an electric field is presented. From the quantum-mechanical wavepacket motion the classical energies at which new orbits bifurcate from the uphill and downhill orbits are obtained. This is an application of the inverse correspondence principle, since the discrete quantum spectrum is used to calculate classical features of the system. It is shown that at every bifurcation the periods of wavepacket motion in the radial and angular-momentum coordinate are commensurable. Therefore, all recurrences seen in electronic wavepacket experiments with Rydberg atoms in an electric field are the direct result of these bifurcations. To illustrate our point, experimental spectra before and after the bifurcation of the so-called orbit are presented.

Atomic electron wave packets studied with a time resolved phase-modulated technique

This paper presents a technique to study wave packet dynamics. The wave packet is excited by two identical laser pulses of which the relative phase is modulated. The probability amplitude excited by the first pulse is either enhanced or reduced due to interference with the amplitude created by the second pulse, depending on the relative phase. The extent to which this enhancement or reduction takes place reflects the overlap between the initial wave function and the wave at the time of arrival of the second pulse. By measuring the modulation of the total excited-state population after the pulse pair, which can be done by extremely efficient methods such as pulse field ionization, the absolute value of the time autocorrelation function of the wave packet is obtained. This technique allowed measurements at a repetition rate of 4 MHz.