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 $t_{\rm rev}$ , at the end of which it resembles its original shape. We study the behavior of Rydberg wave packets on time scales much greater than $t_{\rm rev}$ . 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 $t_{\rm sr} \gg t_{\rm rev}$ with the formation of a wave packet that more closely resembles the initial packet than does the full revival at time $t_{\rm rev}$ . Furthermore, at times that are rational fractions of $t_{\rm sr}$ , we show that the motion of the wave packet is periodic with periodicities that can be expressed as fractions of the revival time $t_{\rm rev}$ . These periodicities indicate a new type of fractional revival, occurring for times much greater than $t_{\rm rev}$ . We also examine the effects of quantum defects and laser detunings on the revival structure of Rydberg wave packets for alkali-metal atoms.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 $t_{\rm rev}$, at the end of which it resembles its original shape. We study the behavior of Rydberg wave packets on time scales much greater than $t_{\rm rev}$. 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 $t_{\rm sr} \gg t_{\rm rev}$ with the formation of a wave packet that more closely resembles the initial packet than does the full revival at time $t_{\rm rev}$. Furthermore, at times that are rational fractions of $t_{\rm sr}$, we show that the motion of the wave packet is periodic with periodicities that can be expressed as fractions of the revival time $t_{\rm rev}$. These periodicities indicate a new type of fractional revival, occurring for times much greater than $t_{\rm rev}$. We also examine the effects of quantum defects and laser detunings on the revival structure of Rydberg wave packets for alkali-metal atoms.

arXiv:quant-ph/9508025Aug 29, 19950 citations

Superrevivals of Rydberg Wave Packets

Robert Bluhm, V. Alan Kostelecký

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.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.

arXiv:quant-ph/9508026Aug 29, 19950 citations

RYDBERG WAVE PACKETS: FRACTIONAL REVIVALS AND CLASSICAL ORBITS

Mark Mallalieu, Carlos R. Stroud

May 1, 19941 citation

Long-term evolution and revival structure of Rydberg wave packets for hydrogen and alkali-metal atoms

Robert Bluhm, V. Alan Kostelecký

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 ${\mathit{t}}_{\mathrm{rev}}$ , 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 ${\mathit{t}}_{\mathrm{rev}}$ . These long-term periodicities result in the autocorrelation function at times greater than ${\mathit{t}}_{\mathrm{rev}}$ having a self-similar resemblance to its structure for times less than ${\mathit{t}}_{\mathrm{rev}}$ . 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 ${\mathit{t}}_{\mathrm{rev}}$ , 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.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 ${\mathit{t}}_{\mathrm{rev}}$, 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 ${\mathit{t}}_{\mathrm{rev}}$. These long-term periodicities result in the autocorrelation function at times greater than ${\mathit{t}}_{\mathrm{rev}}$ having a self-similar resemblance to its structure for times less than ${\mathit{t}}_{\mathrm{rev}}$. 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 ${\mathit{t}}_{\mathrm{rev}}$, 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.

arXiv:quant-ph/9506009Physical Review AJun 1, 199570 citations

Precise manipulation of Rydberg wave packets

B. Wyker, F. B. Dunning, Carlos O Reinhold +2 more

Bulletin of the American Physical SocietyMay 27, 20100 citations

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

t_{\rm rev}

, at the end of which it resembles its original shape. We study the behavior of Rydberg wave packets on time scales much greater than

t_{\rm rev}

. 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

t_{\rm sr} \gg t_{\rm rev}

with the formation of a wave packet that more closely resembles the initial packet than does the full revival at time

t_{\rm rev}

. Furthermore, at times that are rational fractions of

t_{\rm sr}

, we show that the motion of the wave packet is periodic with periodicities that can be expressed as fractions of the revival time

t_{\rm rev}

. These periodicities indicate a new type of fractional revival, occurring for times much greater than

t_{\rm rev}

. We also examine the effects of quantum defects and laser detunings on the revival structure of Rydberg wave packets for alkali-metal atoms.

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.

{\mathit{t}}_{\mathrm{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

{\mathit{t}}_{\mathrm{rev}}

. These long-term periodicities result in the autocorrelation function at times greater than

{\mathit{t}}_{\mathrm{rev}}

having a self-similar resemblance to its structure for times less than

{\mathit{t}}_{\mathrm{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

{\mathit{t}}_{\mathrm{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.