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Journal of Physics B Atomic Molecular and Optical Physics

Observations of the collapse and fractional revival of a Rydberg wavepacket in atomic rubidium

D. R. Meacher, P. E. Meyler, Ifan G. Hughes, P. Ewart

Published Feb 14, 1991• 77 citations
Publisher

Abstract

The authors have excited and detected a radially localized electronic wavepacket in atomic rubidium. The wavepacket is formed of an optically induced coherent superposition of Rydberg states with mean principal quantum number, n=62. The motion of the wavepacket on a classical trajectory is monitored in a time-delayed ionization experiment. The collapse and revival of the classical dynamics is observed. During the period of nonclassical behaviour they observe, for the first time, a partial revival of the wavepacket.

DOI
10.1088/0953-4075/24/3/005

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The authors have excited and detected a radially localized electronic wavepacket in atomic rubidium. The wavepacket is formed of an optically induced coherent superposition of Rydberg states with mean principal quantum number, n=62. The motion of the wavepacket on a classical trajectory is monitored in a time-delayed ionization experiment. The collapse and revival of the classical dynamics is observed. During the period of nonclassical behaviour they observe, for the first time, a partial revival of the wavepacket.
Quantum mechanical wave packet states can approach the classical ideal of a spatially localized particle traveling along a well-defined trajectory. These states offer a system in which the classical limit of quantum atomic theory can be studied. In this work, a wave packet that is radially localized and whose radial motion occurs at the classical orbital period is studied. Despite these strong classical features, the long-term evolution displays the quantum nature of the state. As the wave packet evolves, it becomes dispersed, and the radial motion becomes irregular. However, the wave packet does not remain dispersed, and classical motion returns with the return of the spatial localization. Both the collapse and revival of the wave packet occur because of the quantized nature of the atom. In this experiment, the wave packet was excited to the Rydberg slates by a short, ultraviolet pulse from the ground state of potassium. The probe pulse delay was scanned, and the resulting photo-ionization signal displayed the evolution of the wave packet. The collapse and revival of the radial wave packet were observed.1
We report an observation of the long-term evolution of a radially localized electronic wave packet formed by the coherent superposition of Rydberg states of atomic potassium. Initially, the wave packet can be described classically. Subsequent dephasing of the discrete states in the superposition leads to a loss of spatial localization so that the evolution can no longer be described classically. However, the wave packet revives at a later time. Theory and experiment show good agreement including an accurate measurement of the phase shift of the wave packet on revival.
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 or full revival, which occurs on the time scale trev{\mathit{t}}_{\mathrm{rev}}trev​, 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 trev{\mathit{t}}_{\mathrm{rev}}trev​. These long-term periodicities result in the autocorrelation function at times greater than trev{\mathit{t}}_{\mathrm{rev}}trev​ having a self-similar resemblance to its structure for times less than trev{\mathit{t}}_{\mathrm{rev}}trev​. 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 trev{\mathit{t}}_{\mathrm{rev}}trev​, 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.
At the 1990 UFP conference the observation of several kinds of wave packets was reported [1]. All these wavepackets have in common that the wavefunction is localised due to a coherent superposition of eigenstates. The localised ‘particle’ evolves in course of time. The oscillation time of the wavepacket is determined by the inverse spacing of the states out of which the wavepacket is formed. We reported on the localisation of an atomic electron wavefunction by coherent superposition of Rydberg states. Also the observation of exciton wavepackets was reported, as well as the observations of optic phonons in the time domain. At an earlier conference the CalTech group reported already the observation of the oscillation of vibrational wavepackets in diatomic molecules [2].