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arXiv:quant-ph/9508026

Superrevivals of Rydberg Wave Packets

Robert Bluhm, V. Alan Kostelecký

Published Aug 29, 1995• 0 citations
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Abstract

The revival structure and evolution of Rydberg wave packets are studied on a time scale much greater than the revival time $t_{\rm rev}$. We find a new level of revival structure and periodic motion different from that of the known fractional revivals. The new sequence of revivals culminates with the formation of a wave packet that more closely resembles the initial packet than does the full revival at time $t_{\rm rev}$. We refer to such a revival as a superrevival. We also show that an initial radial wave packet may be described as a type of squeezed state known as a radial squeezed state. Our results apply not only for hydrogenic wave packets, but for wave packets in alkali-metal atoms as well in the context of quantum defect theory.

DOI
10.48550/arxiv.quant-ph/9508026

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Physical Review Letters•Apr 23, 1990•313 citations
The revival structure and evolution of Rydberg wave packets are studied on a time scale much greater than the revival time trevt_{\rm rev}trev​. We find a new level of revival structure and periodic motion different from that of the known fractional revivals. The new sequence of revivals culminates with the formation of a wave packet that more closely resembles the initial packet than does the full revival at time trevt_{\rm rev}trev​. We refer to such a revival as a superrevival. We also show that an initial radial wave packet may be described as a type of squeezed state known as a radial squeezed state. Our results apply not only for hydrogenic wave packets, but for wave packets in alkali-metal atoms as well in the context of quantum defect theory.
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.
After a Rydberg wave packet forms, it is known to undergo a series of collapses and revivals within a time period called the revival time trevt_{\rm rev}trev​, at the end of which it resembles its original shape. We study the behavior of Rydberg wave packets on time scales much greater than trevt_{\rm rev}trev​. We find that after a few revival cycles the wave packet ceases to reform at multiples of the revival time. Instead, a new series of collapses and revivals commences, culminating after a time period tsr≫trevt_{\rm sr} \gg t_{\rm rev}tsr​≫trev​ with the formation of a wave packet that more closely resembles the initial packet than does the full revival at time trevt_{\rm rev}trev​. Furthermore, at times that are rational fractions of tsrt_{\rm sr}tsr​, we show that the motion of the wave packet is periodic with periodicities that can be expressed as fractions of the revival time trevt_{\rm rev}trev​. These periodicities indicate a new type of fractional revival, occurring for times much greater than trevt_{\rm rev}trev​. We also examine the effects of quantum defects and laser detunings on the revival structure of Rydberg wave packets for alkali-metal atoms.
We examine the revival structure of Rydberg wave packets. These wave packets exhibit initial classical periodic motion followed by a sequence of collapse, fractional/full revivals, and fractional/full superrevivals. The effects of quantum defects on wave packets in alkali-metal atoms and a squeezed-state description of the initial wave packets are also described. We then examine the revival structure of Rydberg wave packets in the presence of an external electric field, i.e., the revival structure of Stark wave packets. These wave packets have energies that depend on two quantum numbers and exhibit new types of interference behavior.
The behavior of Hydrogen Rydberg wave packets on time scales much greater than trev was studied.After a few revival cycles the wave packet ceases to reform at multiples of the revival time.Instead,a new series of collapses and revivals commences.Its periodicity is tsr(tsrtrev).The wave packet that forms at time tsr more closely resembles the initial packet than does the full revival packet at time trev.An explanation of these effects is given by constructing autocorrelation function and using the relationship between the wave function and those subsidiary wave functions.
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.