Trojan wavepackets in quantum mechanics equivalent to classical mechanics

Donald Jack Kouri, Youhong Huang, David K. Hoffman

G.J. Papadopoulos

E A Shapiro, Maciej Kaliński, Joseph H. Eberly

We develop a fully quantum-mechanical theory to describe non-circular Trojan-like wavepackets. These correspond to nonlinear resonances in Rydberg hydrogen dressed in a circularly polarized microwave field. The theory is applied to describe adiabatic quantum control of Rydberg states via the wavepackets. The possibility of such quantum control is demonstrated in numerical experiments.

John R. Merrill

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.

Kim Fook Lee