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Physica Scripta

Rydberg Wave Packets and the Classical Limit

Jonathan S. Parker, Carlos R. Stroud

Published Jan 1, 1986• 50 citations
Publisher

Abstract

A method is proposed and analyzed for producing single atom Rydberg states which are nearly as possible classical. It is shown that a picosecond laser pulse can excite a localized wave packet of Rydberg states which propagates like a particle in a classical Kepler orbit. These states are studied numerically and approximate analytic techniques are developed for analyzing their properties.

DOI
10.1088/0031-8949/1986/t12/010

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A method is proposed and analyzed for producing single atom Rydberg states which are nearly as possible classical. It is shown that a picosecond laser pulse can excite a localized wave packet of Rydberg states which propagates like a particle in a classical Kepler orbit. These states are studied numerically and approximate analytic techniques are developed for analyzing their properties.
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.
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.
A series of calculations are presented showing the response of an atom to a picosecond laser pulse that simultaneously excites a number of Rydberg states. A coherent electron wave packet is formed. The packet may disperse and reform repeatedly as its center moves along a classical orbit. The repeated acceleration and deceleration of the wave packet as it moves around the orbit leads to a corresponding variation in the radiation rate of the atom. The result is a complicated pattern of multilevel quantum beats. Examples are shown for various excitation frequencies and pulse durations. Experimental implications are discussed.
The short-pulse dynamics of excitation and stimulated emission between highly excited states (15<n<60)(15<n<60)(15<n<60) is studied with picosecond far-infrared pulses (40--60 $\ensuremath{\mu}\mathrm{m}$) originating from a free electron laser. We measured the excitation of a Rydberg wave packet in rubidium around n=40n=40n=40 excited from a deeper bound $(n\ensuremath{\approx}20)$ Rydberg state by a picosecond far-infrared laser pulse. Moreover, starting from a stationary n=40n=40n=40 state we found that upon irradiating with a short far-infrared laser pulse, adjacent Rydberg states are populated by resonant Raman transfer via a deeper (n=20)(n=20)(n=20) bound state. Finally, we discuss the dynamics of wave-packet excitation at a Cooper minimum in lithium, where sign change of the excitation matrix elements causes excitation at large distances from the atomic core. Possible measurement methods for this effect are discussed and found to yield different information.