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

Physical Review A

Coherent states in a Rydberg atom: Quantum mechanics

C. Cerjan, Ernestine Lee, David Farrelly, T. Uzer

Published Mar 1, 1997• 21 citations
Publisher

Abstract

We present the quantal dynamics of electronic wave packets in the hydrogen atom in the presence of circularly polarized microwave and magnetic fields in regions of classical stability. Whereas wave packets may disperse without the stabilizing influence of a magnetic field, in its presence stable motion can be maintained for wave packets that are localized either at global equilibria that are either a maximum or minimum in a zero-velocity surface. Because these extrema are locally harmonic their vacuum states are truly coherent states in the original sense of Schr\"odinger.

DOI
10.1103/physreva.55.2222

Related papers

Coherent states in a Rydberg atom: Classical mechanics

Ernestine Lee, Andrea F. Brunello, David Farrelly

The interaction of a hydrogen or Rydberg atom with a circularly polarized microwave field leads to the creation of global equilibrium points that may be stable or unstable depending on the particulars of the applied field. The additional application of a magnetic field, perpendicular to the plane of polarization, can be used to manipulate both the nature and the stability of these points. We show that stable three-dimensional motion can be maintained that is localized at either a maximum or a minimum in the corresponding surface of zero velocity. At these equilibria, the zero-velocity surface may be locally quadratic in coordinates and stable harmonic-oscillator-like, nondispersive, coherent states can be supported. As the fields are varied, repeated order-chaos transitions may be observed, including various passages through rigorously integrable limits. Classical simulations are presented for a range of field strengths, and the effects of deviations of the microwave field from exactly circular polarization (i.e., elliptical polarization) are examined using a pulsating zero-velocity surface.

Physical Review A•Mar 1, 1997•32 citations

The Classical Atom: Stabilization of Electronic Trojan Wavepackets

David Farrelly, Ernestine A. Lee, T. Uzer

This article demonstrates that coherent states in Rydberg atoms can be produced and stabilized by combining a circularly polarized microwave field with a static, perpendicular magnetic field. These electronic wavepackets owe their stability to atomic analogs of the Lagrange equilibria which confine Jupiter's Trojan asteroids. While these “Trojan” wavepackets may slowly decay due to tunneling, a more significant source of dispersion will arise if the tails of the wavepacket penetrate appreciably into the non-linear or chaotic parts of phase space. In the laboratory frame, if these dispersive factors can be minimized — and this may be accomplished using magnetic fields — the electronic wavepacket will travel along a circular Kepler orbit while remaining localized radially and angularly for a finite — but large — number of Kepler periods. In this sense, the system is a classical Bohr atom.

Fortschritte der Physik•May 1, 2002•2 citations

A Wave Packet Can Be a Stationary State

Dominique Delande, Jakub Zakrzewski, Andreas Buchleitner

We establish the existence of strongly localized wave packets tracing without dispersion the classical dynamics of a Rydberg electron in a circularly polarized microwave field over up to 10 6 periods of the driving field, which at the same time are single eigenstates of the atom dressed by the microwave field. These “single-state wave packets” are shown to be robust towards small changes of the external field and can be prepared experimentally.

Europhysics Letters (EPL)•Oct 10, 1995•41 citations

Single Atom Quasi-Penning Trap

Ernestine Lee, Andrea F. Brunello, David Farrelly

The combination of a circularly polarized microwave field and a magnetic field can be used to create a global equilibrium point---an outer minimum---in the electronic dynamics of Rydberg atoms. Stable motion can be maintained at this minimum and the Rydberg electron is localized both radially and angularly while moving on a circular Kepler orbit in a region of space that excludes the nucleus.

Physical Review Letters•Nov 13, 1995•29 citations

Nonspreading Electronic Wave Packets and Conductance Fluctuations

Jakub Zakrzewski, Dominique Delande, Andreas Buchleitner

We find strongly localized wave packets tracing without dispersion the classical dynamics of a Rydberg electron in a circularly polarized microwave field using a full 3D quantum calculation. These wave packets are single eigenstates of the atom dressed by the microwave field and are very stable against ionization. Their widths fluctuate with microwave amplitude and/or frequency realizing an optical analog of the conductance fluctuations in mesoscopic systems. Similar behavior is observed for linear microwave polarization. We show that such behavior is expected when classical nonlinear resonances are important in an atomic system.

Physical Review Letters•Nov 27, 1995•43 citations

New States of Hydrogen in a Circularly Polarized Electromagnetic Field

Maciej Kaliński, Joseph H. Eberly

We predict the existence in hydrogen of stable nonspreading Rydberg wave packet states that have no classical counterparts. We show their time-dependent creation from circular Rydberg states in numerical simulations. These states are both angularly and radially localized exactly in antiphase from the corresponding nonspreading (so-called Trojan) packet position and are stabilized by quantum interference.

Physical Review Letters•Sep 16, 1996•41 citations
We present the quantal dynamics of electronic wave packets in the hydrogen atom in the presence of circularly polarized microwave and magnetic fields in regions of classical stability. Whereas wave packets may disperse without the stabilizing influence of a magnetic field, in its presence stable motion can be maintained for wave packets that are localized either at global equilibria that are either a maximum or minimum in a zero-velocity surface. Because these extrema are locally harmonic their vacuum states are truly coherent states in the original sense of Schr"odinger.
The interaction of a hydrogen or Rydberg atom with a circularly polarized microwave field leads to the creation of global equilibrium points that may be stable or unstable depending on the particulars of the applied field. The additional application of a magnetic field, perpendicular to the plane of polarization, can be used to manipulate both the nature and the stability of these points. We show that stable three-dimensional motion can be maintained that is localized at either a maximum or a minimum in the corresponding surface of zero velocity. At these equilibria, the zero-velocity surface may be locally quadratic in coordinates and stable harmonic-oscillator-like, nondispersive, coherent states can be supported. As the fields are varied, repeated order-chaos transitions may be observed, including various passages through rigorously integrable limits. Classical simulations are presented for a range of field strengths, and the effects of deviations of the microwave field from exactly circular polarization (i.e., elliptical polarization) are examined using a pulsating zero-velocity surface.
This article demonstrates that coherent states in Rydberg atoms can be produced and stabilized by combining a circularly polarized microwave field with a static, perpendicular magnetic field. These electronic wavepackets owe their stability to atomic analogs of the Lagrange equilibria which confine Jupiter's Trojan asteroids. While these “Trojan” wavepackets may slowly decay due to tunneling, a more significant source of dispersion will arise if the tails of the wavepacket penetrate appreciably into the non-linear or chaotic parts of phase space. In the laboratory frame, if these dispersive factors can be minimized — and this may be accomplished using magnetic fields — the electronic wavepacket will travel along a circular Kepler orbit while remaining localized radially and angularly for a finite — but large — number of Kepler periods. In this sense, the system is a classical Bohr atom.
We find strongly localized wave packets tracing without dispersion the classical dynamics of a Rydberg electron in a circularly polarized microwave field using a full 3D quantum calculation. These wave packets are single eigenstates of the atom dressed by the microwave field and are very stable against ionization. Their widths fluctuate with microwave amplitude and/or frequency realizing an optical analog of the conductance fluctuations in mesoscopic systems. Similar behavior is observed for linear microwave polarization. We show that such behavior is expected when classical nonlinear resonances are important in an atomic system.