Quantum theory provides the basis for the physical description of Nature on a microscopic level, i.e., in terms of its basic constituents such as elementary particles, atoms, and molecules. However, the macroscopic world, that surrounds us and is built up from these constituents, is adequately explained in terms of classical physics, which in many instances appears to be very different from or even contradictory to the laws of quantum theory. The study of systems, that are situated on the border between the microscopic and macroscopic world, is thus crucial in order to reconcile our views of classical and quantum physics.
Rydberg atoms are characterized by one or more electrons being excited to high-lying states right below an ionization threshold (in a hydrogen atom, e.g., these are the states with a very high radial quantum number n). Due to their large spatial extension, these electronic Rydberg systems are ideally suited to explore the border area between the microscopic and macroscopic regime.
The interplay between classical and quantum aspects in their behavior becomes particularly apparent when studying the time-dependent dynamics of Rydberg wave packets. Such wave packets are localized quantum states of the excited Rydberg electron and consist of a superposition of a large number of electronic eigenstates. Far away from the nucleus and the other atomic electrons, the center of the wave packet moves on a Kepler trajectory almost like a classical particle. The true quantum-mechanical nature of the wave packet, however, becomes manifest in its interaction with the other atomic electrons and its external environment, e.g. a laser field, and in the effects of collapse and revival, where the wave packet first broadens but eventually regains its original shape.
The members of our group have elucidated various aspects of the interplay of classical and quantum-mechanical behavior in the dynamics of electronic Rydberg systems which are listed below.
The technique of semiclassical path representations constitutes the main building block in our description of electronic Rydberg wave packets. It rests on the observation that there exist two distinct spatial regimes that determine the electronic dynamics: Close to the atomic nucleus, the Rydberg electron strongly feels the presence of the other electrons. These complicated interactions can be expressed concisely in terms of a scattering matrix depending on a small number of quantum defect parameters, only.
Beyond the inner region, the Rydberg electron is subject only to the Coulomb force exerted by the ionic core. The dynamics in this area are described adequately with the help of semiclassical methods that use as input the properties of the classical trajectories along which the electron can travel. Combining the descriptions of the inner and the outer region yields the semiclassical path representation of the wave packet dynamics. It provides a quantitative, yet intuitive description of the electronic time evolution.
The semiclassical path method was successfully applied to describe multichannel systems and autoionization, wave packet motion in static electric and magnetic fields, bifurcation phenomena, laser interactions, isolated core excitations and decoherence phenomena.
G. Alber, in The Physics and Chemistry of Wave Packets,
edited by J. A. Yeazell and T. Uzer (Wiley, N. Y., 2000)
O. Zobay and G. Alber, Progress of Physics 46, 3 (1998)
M. W. Beims and G. Alber, J. Phys. B 29, 4139 (1996)
G. Alber and P. Zoller, Phys. Rep. 199, 231 (1991)
G. Alber, Z. Phys. D. 14, 307 (1989)
G. Alber and P. Zoller, Phys. Rev. A 37, 377 (1988)
Half-cycle pulses (HCPs) are unipolar, high-power electromagnetic pulses whose duration can range from the subpicosecond to the nanosecond regime. Over the recent years, HCPs have proven to be a powerful spectroscopic tool for the investigation of Rydberg wave packet dynamics. Two main features contribute to their attractivity: they can ionize the electron at each point of its orbit and their effect can often be modeled simply in terms of an instantaneous momentum change of the electron (sudden-impact approximation).
We have developed a multidimensional semiclassical description of excitation of a weakly bound Rydberg electron by a half-cycle pulse. It connects the quantum evolution of the Rydberg electron to its underlying classical evolution on a quantitative level. The approach is nonperturbative and can be applied to HCPs of any shape and duration. On the basis of this approach we have investigated energy- and angle-resolved ionization spectra. It was shown that within the validity regime of the sudden-impact regime, these spectra are dominated by semiclassical interference phenomena of the glory and rainbow type.
Central to our understanding of the connection between quantum and classical physics is the notion of decoherence, which leads to the suppression of quantum behavior in macroscopic objects. Although decoherence has been studied for a number of different systems, a complete understanding of decoherence effects on wave packets is still missing.
To perform a step in this direction, we have performed a thorough investigation of the resonant excitation of Rydberg electrons in intense, fluctuating laser fields. Such laser fluctuations lead to a destruction of quantum coherence in the electronic density matrix. Our studies showed that generic long-time phenomena, such as diffusion and stochastic ionization, can be expected to occur under these circumstances. Quantitatively, these novel fluctuation-induced effects are characterized by non-exponential time evolutions whose power law dependencies were determined analytically.
B. Eggers and G. Alber, J. Phys. B 34, 4053 (2001)
B. Eggers and G. Alber, J. Phys. B 32, 1019 (1999)
G. Alber and B. Eggers, Optics Express 1, 203 (1997)
G. Alber and B. Eggers, Phys. Rev. A 56, 820 (1997)
Isolated core excitations constitute a particular kind of atomic excitation process that involves two valence electrons. Typically, an isolated core excitation proceeds in a sequence of steps: at first, one electron is excited to a Rydberg state with one or more laser pulses. Subsequently, a further laser pulse excites the second electron to an energetically low-lying state of the atomic core. The Rydberg electron acts as a spectator and is affected by the core transition only through the process of shakeup, i.e., the readjustment of the Rydberg electron to the modified core configuration.
In our work, we considered the effect of continuously driven Rabi oscillations of the ionic core on the dynamics of a previously prepared Rydberg wave packet. The interaction between the laser-driven core and the Rydberg electron can be described in terms of a "dressed" scattering matrix. Combining this result with the technique of semiclassical path representations yields a quantitative, yet intuitive description of the wave packet dynamics. Our approach could be extended to describe the influence of spontaneous emission of the core on the wave packet dynamics as well as the effect of the Rydberg electron on the atomic diffraction in a standing-wave laser field.
O. Zobay and G. Alber, Progress of Physics 46, 3 (1998)
O. Zobay and G. Alber, Phys. Rev. A 56, 3897 (1997)
O. Zobay and G. Alber, Phys. Rev. A 54, 5361 (1996)
O. Zobay and G. Alber, Phys. Rev. A. 52, 541 (1995)
Prof. Dr. Gernot Alber
Institut für Angewandte Physik
64289 Darmstadt, Germany
+49-6151/16-20400 (fax: 20402)