Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Supersymmetry and radial squeezed states for Rydberg wave packets

Robert Bluhm, V. Alan Kostelecký

Published May 1, 1994• 0 citations
OpenAlex

Abstract

Atomic supersymmetry provides an analytical effective-potential model useful for describing certain aspects of Rydberg atoms. Experiments have recently demonstrated the existence of Rydberg wave packets localized in the radial coordinated with p-state angular distribution. This paper shows how atomic supersymmetry can be used to treat radial Rydberg wave packets via a particular analytical type of squeezed state, called a radial squeezed state.

Related papers

Radial squeezed states and Rydberg wave packets

Robert Bluhm, V. Alan Kostelecký

We outline an analytical framework for the treatment of radial Rydberg wave packets produced by short laser pulses in the absence of external electric and magnetic fields. Wave packets of this type are localized in the radial coordinates and have p-state angular distributions. We argue that they can be described by a particular analytical class of squeezed states, called radial squeezed states. For hydrogenic Rydberg atoms, we discuss the time evolution of the corresponding hydrogenic radial squeezed states. They are found to undergo decoherence and collapse, followed by fractional and full revivals. We also present their uncertainty product and uncertainty ratio as functions of time. Our results show that hydrogenic radial squeezed states provide a suitable analytical description of hydrogenic Rydberg atoms excited by short-pulsed laser fields.

arXiv:quant-ph/9508019•Physical Review A•Dec 1, 1993•14 citations

Keplerian squeezed states and Rydberg wave packets

Robert Bluhm, V. Alan Kostelecký, Bogdan Tudose

We construct minimum-uncertainty solutions of the three-dimensional Schr\"odinger equation with a Coulomb potential. These wave packets are localized in radial and angular coordinates and are squeezed states in three dimensions. They move on elliptical Keplerian trajectories and are appropriate for the description of the corresponding Rydberg wave packets, the production of which is the focus of current experimental effort. We extend our analysis to incorporate the effects of quantum defects in alkali-metal atoms, which are used in experiments. \textcopyright{} 1996 The American Physical Society.

arXiv:quant-ph/9510023•Physical Review A•Feb 1, 1996•21 citations

Elliptical squeezed states and Rydberg wave packets

Robert Bluhm, V. Alan Kostelecký, Bogdan Tudose

We present a theoretical construction for closest-to-classical wave packets localized in both angular and radial coordinates and moving on a keplerian orbit. The method produces a family of elliptical squeezed states for the planar Coulomb problem that minimize appropriate uncertainty relations in radial and angular coordinates. The time evolution of these states is studied for orbits with different semimajor axes and eccentricities. The elliptical squeezed states may be useful for a description of the motion of Rydberg wave packets excited by short-pulsed lasers in the presence of external fields, which experiments are attempting to produce. We outline an extension of the method to include certain effects of quantum defects appearing in the alkali-metal atoms used in experiments.

arXiv:quant-ph/9509010•Physical Review A•Sep 1, 1995•34 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.

arXiv:quant-ph/9508026•Aug 29, 1995•0 citations

Spatially localized Rydberg atom wave packets

John A. Yeazell, Carlos R. Stroud

The quantum theory of atoms is based on a Hamiltonian which is just that of the classical Kepler theory of planetary orbits. In spite of this common foundation, the predictions of the quantum theory ordinarily do not much resemble those of the classical theory. Even in the limit of large quantum numbers the energy eigenstates of quantum theory do not look at all like the classical elliptical orbits. Recently, Parker and Stroud1 showed that it is possible to excite a Rydberg atomic wave packet localized in the radial coordinate. Also, Yeazell and Stroud2 showed that a wave packet localized in the angular coordinates can be formed. Both wave packets exhibit an evolution describable, at least in part, by classical theory. However, neither wave packet truly corresponds to a wave packet traveling in a classical elliptical orbit. We discuss the manner in which such a wave packet might be formed using a short-pulsed laser and arf dressing field. The evolution of the resulting wave packet is compared with that of its classical counterpart.

Annual Meeting Optical Society of America•Jan 1, 1987•0 citations

Rydberg atom wave packets localized in the angular coordinates

John A. Yeazell, Carlos R. Stroud

The quantum theory of atoms is based on a Hamiltonian which is just that of the classical Kepler theory of planetary orbits. In spite of this common foundation, the predictions of quantum theory ordinarily do not much resemble those of classical theory. Even in the limit of large quantum numbers the energy eigenstates of quantum theory do not look at all like the classical elliptical orbits. Recently, Parker and Stroud1 have shown that it is possible to excite a Rydberg atom wave packet whose radial dependence resembles the classical ideal of a particle traveling in an elliptical orbit. In this paper we discuss the formation of a wave packet in the polar and azimuthal angles by the coherent excitation of Rydberg states with the same principal quantum, but with a distribution of the angular momentum quantum numbers. When this wave packet is formed of the Rydberg states of an alkali atom the connection with classical theory is again striking. The wave packet precesses due to the core polarization, just as the classical elliptical orbit precesses due to an added r–4 perturbing potential.

Annual Meeting Optical Society of America•Jan 1, 1986•0 citations
Atomic supersymmetry provides an analytical effective-potential model useful for describing certain aspects of Rydberg atoms. Experiments have recently demonstrated the existence of Rydberg wave packets localized in the radial coordinated with p-state angular distribution. This paper shows how atomic supersymmetry can be used to treat radial Rydberg wave packets via a particular analytical type of squeezed state, called a radial squeezed state.
We outline an analytical framework for the treatment of radial Rydberg wave packets produced by short laser pulses in the absence of external electric and magnetic fields. Wave packets of this type are localized in the radial coordinates and have p-state angular distributions. We argue that they can be described by a particular analytical class of squeezed states, called radial squeezed states. For hydrogenic Rydberg atoms, we discuss the time evolution of the corresponding hydrogenic radial squeezed states. They are found to undergo decoherence and collapse, followed by fractional and full revivals. We also present their uncertainty product and uncertainty ratio as functions of time. Our results show that hydrogenic radial squeezed states provide a suitable analytical description of hydrogenic Rydberg atoms excited by short-pulsed laser fields.
We construct minimum-uncertainty solutions of the three-dimensional Schr\"odinger equation with a Coulomb potential. These wave packets are localized in radial and angular coordinates and are squeezed states in three dimensions. They move on elliptical Keplerian trajectories and are appropriate for the description of the corresponding Rydberg wave packets, the production of which is the focus of current experimental effort. We extend our analysis to incorporate the effects of quantum defects in alkali-metal atoms, which are used in experiments. \textcopyright{} 1996 The American Physical Society.
We present a theoretical construction for closest-to-classical wave packets localized in both angular and radial coordinates and moving on a keplerian orbit. The method produces a family of elliptical squeezed states for the planar Coulomb problem that minimize appropriate uncertainty relations in radial and angular coordinates. The time evolution of these states is studied for orbits with different semimajor axes and eccentricities. The elliptical squeezed states may be useful for a description of the motion of Rydberg wave packets excited by short-pulsed lasers in the presence of external fields, which experiments are attempting to produce. We outline an extension of the method to include certain effects of quantum defects appearing in the alkali-metal atoms used in experiments.
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.
The quantum theory of atoms is based on a Hamiltonian which is just that of the classical Kepler theory of planetary orbits. In spite of this common foundation, the predictions of the quantum theory ordinarily do not much resemble those of the classical theory. Even in the limit of large quantum numbers the energy eigenstates of quantum theory do not look at all like the classical elliptical orbits. Recently, Parker and Stroud1 showed that it is possible to excite a Rydberg atomic wave packet localized in the radial coordinate. Also, Yeazell and Stroud2 showed that a wave packet localized in the angular coordinates can be formed. Both wave packets exhibit an evolution describable, at least in part, by classical theory. However, neither wave packet truly corresponds to a wave packet traveling in a classical elliptical orbit. We discuss the manner in which such a wave packet might be formed using a short-pulsed laser and arf dressing field. The evolution of the resulting wave packet is compared with that of its classical counterpart.
The quantum theory of atoms is based on a Hamiltonian which is just that of the classical Kepler theory of planetary orbits. In spite of this common foundation, the predictions of quantum theory ordinarily do not much resemble those of classical theory. Even in the limit of large quantum numbers the energy eigenstates of quantum theory do not look at all like the classical elliptical orbits. Recently, Parker and Stroud1 have shown that it is possible to excite a Rydberg atom wave packet whose radial dependence resembles the classical ideal of a particle traveling in an elliptical orbit. In this paper we discuss the formation of a wave packet in the polar and azimuthal angles by the coherent excitation of Rydberg states with the same principal quantum, but with a distribution of the angular momentum quantum numbers. When this wave packet is formed of the Rydberg states of an alkali atom the connection with classical theory is again striking. The wave packet precesses due to the core polarization, just as the classical elliptical orbit precesses due to an added r–4 perturbing potential.