dorsal/arxiv
View SchemaLong-Term Evolution and Revival Structure of Rydberg Wave Packets for Hydrogen and Alkali-Metal Atoms
| Authors | Robert Bluhm, Alan Kostelecky |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9506009 |
| URL | https://arxiv.org/abs/quant-ph/9506009 |
| DOI | 10.1103/PhysRevA.51.4767 |
| Journal | Phys.Rev.A51:4767-4786,1995 |
Abstract
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.
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"abstract": "This paper begins with an examination of the revival structure and long-term\nevolution of Rydberg wave packets for hydrogen. We show that after the initial\ncycle of collapse and fractional/full revivals, which occurs on the time scale\n$t_{\\rm rev}$, a new sequence of revivals begins. We find that the structure of\nthe new revivals is different from that of the fractional revivals. The new\nrevivals are characterized by periodicities in the motion of the wave packet\nwith periods that are fractions of the revival time scale $t_{\\rm rev}$. These\nlong-term periodicities result in the autocorrelation function at times greater\nthan $t_{\\rm rev}$ having a self-similar resemblance to its structure for times\nless than $t_{\\rm rev}$. The new sequence of revivals culminates with the\nformation of a single wave packet that more closely resembles the initial wave\npacket than does the full revival at time $t_{\\rm rev}$, i.e., a superrevival\nforms. Explicit examples of the superrevival structure for both circular and\nradial wave packets are given. We then study wave packets in alkali-metal\natoms, which are typically used in experiments. The behavior of these packets\nis affected by the presence of quantum defects that modify the hydrogenic\nrevival time scales and periodicities. Their behavior can be treated\nanalytically using supersymmetry-based quantum-defect theory. We illustrate our\nresults for alkali-metal atoms with explicit examples of the revival structure\nfor radial wave packets in rubidium.",
"arxiv_id": "quant-ph/9506009",
"authors": [
"Robert Bluhm",
"Alan Kostelecky"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.51.4767",
"journal_ref": "Phys.Rev.A51:4767-4786,1995",
"title": "Long-Term Evolution and Revival Structure of Rydberg Wave Packets for Hydrogen and Alkali-Metal Atoms",
"url": "https://arxiv.org/abs/quant-ph/9506009"
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