Physica Scripta

The role of the quantum defect and of high-order dispersion in rydberg wave packets

Jeroen Wals, Helen H. Fielding, H. B. van Linden van den Heuvell

Published Jan 1, 1995• 26 citations

Abstract

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.

DOI: 10.1088/0031-8949/1995/t58/007

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

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Physica Scripta

The role of the quantum defect and of high-order dispersion in rydberg wave packets

Jeroen Wals, Helen H. Fielding, H. B. van Linden van den Heuvell

Published Jan 1, 1995• 26 citations

Publisher

Abstract

DOI: 10.1088/0031-8949/1995/t58/007

Related papers

Revivals of Rydberg Wave Packets

Robert Bluhm, V. Alan Kostelecký, Bogdan Tudose

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.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.

arXiv:quant-ph/9711073Physics of Atomic NucleiNov 28, 19972 citations

The Revival Structure of Rydberg Wave Packets Beyond the Revival Time

Robert Bluhm, V. Alan Kostelecký

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

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

Interfering Rydberg wave packets in Na

Robert Carley, Elizabeth Durrell Boleat, Russell S. Minns +2 more

This paper presents an experimental and theoretical analysis of quantum interference between Rydberg wave packets in Na. Pairs of phase-locked wave packets manipulate the total orbital angular momentum of Na Rydberg atoms. Initially, the wave packet is composed of a superposition of s and d Rydberg series. Exploitation of the difference between the quantum defects of the two series allows one to predict the phase of the second wave packet required to engineer specific angular momentum compositions within the resultant wave packet. Experimentally, this final quantum state distribution is analysed in the frequency domain using state-selective field ionization and in the time domain using the optical Ramsey method. The theoretical calculations show how the phase difference between pairs of optical pulses is linked to the corresponding Rydberg frequency spectrum, therefore enabling the control of the quantum state composition of the wave packets. Finally, it is shown that by intuitively chirping one of the laser pulses it is possible to compensate for the dispersion of the wave packet and improve the effectiveness of the angular momentum control.This paper presents an experimental and theoretical analysis of quantum interference between Rydberg wave packets in Na. Pairs of phase-locked wave packets manipulate the total orbital angular momentum of Na Rydberg atoms. Initially, the wave packet is composed of a superposition of s and d Rydberg series. Exploitation of the difference between the quantum defects of the two series allows one to predict the phase of the second wave packet required to engineer specific angular momentum compositions within the resultant wave packet. Experimentally, this final quantum state distribution is analysed in the frequency domain using state-selective field ionization and in the time domain using the optical Ramsey method. The theoretical calculations show how the phase difference between pairs of optical pulses is linked to the corresponding Rydberg frequency spectrum, therefore enabling the control of the quantum state composition of the wave packets. Finally, it is shown that by intuitively chirping one of the laser pulses it is possible to compensate for the dispersion of the wave packet and improve the effectiveness of the angular momentum control.

Journal of Physics B Atomic Molecular and Optical PhysicsJun 6, 200525 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

Observation of quantum features in the evolution of a Rydberg wave packet

John A. Yeazell, Carlos R. Stroud

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.1Quantum 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

Annual Meeting Optical Society of AmericaJan 1, 19900 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.

{\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.

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.