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Physical Review A

Coherent states in a Rydberg atom: Classical mechanics

Ernestine Lee, Andrea F. Brunello, David Farrelly

Published Mar 1, 1997• 32 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.55.2203

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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.
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.
A classical study of the dynamics of atomic Rydberg states interacting with both elliptically and circularly polarized microwave fields is presented. In recent experiments, enhanced ionization rates were observed in elliptically as opposed to circularly polarized fields. A classical phase-space simulation provides good qualitative agreement with experimental findings. These results are explained in terms of the breakdown of almost conserved quantities as the polarization of the field is changed from circular to elliptical.
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.