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Physical Review Letters

Observation of quasi-Landau wave packets

L. Marmet, H. Held, Georg A. Raithel, John A. Yeazell, HERBERT WALTHER

Published Jun 13, 1994• 60 citations
Publisher

Abstract

Atomic wave packets are produced in strong magnetic fields by exciting rubidium atoms with a short UV laser pulse. The strength of the magnetic field is varied from 0 to 3.3 T. In a classical model of these Rydberg atoms, this variation leads to a progression of the system from a regime of regular motion to one where chaotic motion dominates. The evolution of the wave packet is observed using a phase-sensitive technique and is compared to the predictions of a semiclassical model. The effect of an electric field, applied parallel to the magentic field, is also studied. As the electric field is increased, significant changes occur that are due in part to the appearance of new orbits.

DOI
10.1103/physrevlett.72.3779

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Atomic wave packets are produced in strong magnetic fields by exciting rubidium atoms with a short UV laser pulse. The strength of the magnetic field is varied from 0 to 3.3 T. In a classical model of these Rydberg atoms, this variation leads to a progression of the system from a regime of regular motion to one where chaotic motion dominates. The evolution of the wave packet is observed using a phase-sensitive technique and is compared to the predictions of a semiclassical model. The effect of an electric field, applied parallel to the magentic field, is also studied. As the electric field is increased, significant changes occur that are due in part to the appearance of new orbits.
Quantum mechanical wave packet states can approach the classical ideal of a spatially localized particle traveling along a well-defined trajectory. These states offer a system in which the classical limit of quantum atomic theory can be studied. In this work, a wave packet that is radially localized and whose radial motion occurs at the classical orbital period is studied. Despite these strong classical features, the long-term evolution displays the quantum nature of the state. As the wave packet evolves, it becomes dispersed, and the radial motion becomes irregular. However, the wave packet does not remain dispersed, and classical motion returns with the return of the spatial localization. Both the collapse and revival of the wave packet occur because of the quantized nature of the atom. In this experiment, the wave packet was excited to the Rydberg slates by a short, ultraviolet pulse from the ground state of potassium. The probe pulse delay was scanned, and the resulting photo-ionization signal displayed the evolution of the wave packet. The collapse and revival of the radial wave packet were observed.1
This paper reports on the investigation of excitation spectra of rubidium Rydberg atoms in crossed electric and magnetic fields. The quasi-Landau spectra were evaluated and their Fourier transforms calculated. The scaled spectral scans used for this purpose were obtained by changing the electric and magnetic fields as well as the laser frequency in an appropriate way. The observed resonances could be explained completely by semiclassical orbits. Only orbits showing overlap with the ground-state wave function are observed. The polarization dependence of certain components in the Fourier spectra can be explained by the shape of the semiclassical orbits. The electric dipole moments of the atoms resulting from the shift of the quasi-Landau structures in a changing electric field agree quite well with the corresponding semiclassical orbits.
In this chapter experiments on rubidium Rydberg atoms in external fields are reviewed [1 – 8]. In the first part results on the interaction of microwave radiation with rubidium Rydberg atoms are described. The Rydberg atoms interact with a microwave pulse of a well-defined duration. When applying coherent microwave radiation with a frequency exceeding a certain value, the experimentally observed microwave field strength at which 10% of the atoms are ionized has to be much larger than the value found by classical trajectory calculations. The atoms are stabilized by the dynamical localization. An extremely weak microwave broadband noise which is added to the coherent wave at least partially destroys the localization. This phenomenon depends on the bandwidth of the added noise. In further experiments the dependence of the 10% ionization microwave field strength on the duration τ of the microwave pulse has been investigated. For increasing noise level the 10% ionization field strength ∈ 0.1 develops from a behavior ∈ 0.1 ∼ τ −1/4 to a ∈ 0.1 ∼ τ −1/2 dependence, which is characteristic for a classical diffusion process. The second part of the chapter deals with experiments in strong static crossed electric and magnetic fields. Below as well as above the ionization energy the observed quasi-Landau(QL)-resonances are explained using classical trajectories. The ionization behavior of the QL-resonances is clearly influenced by the spatial structure of the associated classical orbits. In further experiments the dependence of the observed ionization energy on the magnetic field was investigated in the presence of a fixed static electric field.
We calculate spectra and wave functions of Rydberg atoms in strong magnetic fields using adiabatic basis sets, which reflect the different time scales of the electronic motion parallel and transverse to the magnetic field. For large absolute values of the azimuthal quantum number m, nonadiabatic corrections are found to be negligible, and the adiabatic basis states and their energies are exact solutions. With decreasing value of ∣m∣,|m|,∣m∣, the system turns nonadiabatic, and the statistical behavior of the spectra changes from being consistent with classically regular to being consistent with classically chaotic motion. A relation describing the parameter region in which this transition occurs is obtained.
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.