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Physical Review A

Rydberg wave packets on elliptical orbits

E. A. Shapiro, Paolo Bellomo

Published Aug 1, 1999• 5 citations
Publisher

Abstract

We predict and confirm numerically the existence of localized Rydberg wave packets that travel on classical elliptical trajectories with negligible spreading. These wave packets are supported by a resonant circularly polarized microwave field, and we study them by a semiclassical action-angle representation.
DOI
10.1103/physreva.60.1403

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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.
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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 results of numerical simulation of the Rydberg states laser excitation for the purpose of the forming of localized wave packets, are provided. The action of linear and circularly polarized fields upon an atom is considered for different time dependencies of the pulse envelope. The form and the properties of the obtained packet, constructed from eigen states with low orbital and magnetic quantum numbers have been analyzed. The obtained results are in agreement with the results provided by other authors.