Research activities

In the last decade, experimental techniques like photodetachment and photoionization microscopy arrived that allow us to directly observe how photoelectrons coherently spread in external fields. Because the electron wave is made up from charged particles, it is easy to influence and control their motion by applying electric and magnetic fields. Although the potentials involved (uniform electric and magnetic fields, the Coulomb field) are very simple, and permit a largely analytic description of the electron motion, these systems harbor a surprisingly rich set of features that often has only been partially explained theoretically. — Examples include photodetachment in an electric field, featuring the most striking demonstration of two-path interference using matter waves to date; photodetachment in parallel fields, where the fields may cause complete suppression of the photoeffect, and an interesting structure of caustic surfaces (boundaries of classical motion) is present; and photoionization in parallel fields, a classically chaotic process that should be fairly amenable to experiment. An important technique in analyzing these systems is the multidimensional semiclassical approximation, a method that seeks to explain the features seen in the quantum mechanical cross sections in terms of the classical electron trajectories. Modern mathematical catastrophe theory is also a closely related subject.

In quantum scattering, it is at times convenient to separate the process that "generates" an electron wave from its subsequent motion under the influence of external and internal forces. To accommodate this, we introduce inhomogeneous "source terms" into the Schrödinger equation, akin to charges and currents in electrodynamics. We have successfully used the versatile source method to describe a variety of scattering processes. The list includes near-threshold photodetachment (see above), but also scanning tunneling microscopy (STM) — here we replace the tip with a pointlike electron source and calculate the conductivity of the tip-surface system; the continuous atom laser, where we studied the coherent motion of a Bose-Einstein condensate (BEC) under the influency of gravity to obtain its beam profile; field emission; and the properties of two-dimensional electron gases (2DEG) in the presence of crossed electric and magnetic fields. Here, the source formalism yields a quantized conductivity similar to the one seen in the quantum Hall effect.

Random walk processes lie at the heart of many important problems in physics. I have studied analytical properties of the continuous persistent random walk in two dimensions (where the directions of adjacent steps are correlated), and self-avoiding walks in two and three dimensions that are based on the rotational isomeric state (RIS) model. These models find application in the statistics of polymer chains and provide an explanation for the elastic properties of single polymer strands. — Diffusion is another process that is microscopically described by a (discrete) random walk. In realistic diffusion models, the hopping rates for a particle depend on the occupation of the neighboring sites due to particle-particle interactions. I developed an analytic model for diffusion on a one-dimensional chain of sites based on the canonical ensemble; starting from a master equation, the probability to find the system in a specific configuration is calculated from the eigenstates and eigenvalues of the evolution operator.

The micromaser setup consists of a beam of excited atoms traversing a superconducting microwave cavity that is exactly tuned to one of the atomic transition frequencies, together with detectors for atoms leaving the cavity in either state. This device allows us to examine cavity quantum electrodynamics, i.e., the interaction of electromagnetic waves and atoms, under nearly ideal conditions. I performed an inquiry into the statistics of atomic pattern probabilities in a simple operation mode of the micromaser, and also discussed the possible usage of this device as a "quantum clock" that yields the traversal time of a quantum particle in a potential barrier (see below).

The tunneling time problem concerns the amount of time spent by a quantum particle in a given sector of space, in particular the duration of tunneling events. Unlike a classical particle that is either reflected off a potential barrier, or transmitted over it, there are finite probabilities that a quantum particle is reflected and transmitted, and it seems natural that both processes should be associated with a certain duration, the reflection and transmission time scales. Despite decades of study, the nature of these tunneling times is still controversial, and while some conceptual framework emerged, consensus on quantum time scales of motion has not been achieved. My work tries to identify sensible definitions, and practical methods to extract the tunneling times, and seeks to establish relationships between the various proposals that have been put forward.