M. Glück’s research while affiliated with Rheinland-Pfälzische Technische Universität Kaiserslautern-Landau and other places

The optical properties of an electrically biased semiconductor superlattice are strongly influenced by coupling to other bands. As these coupling mechanisms depend on the strength of the applied electric field, we find a distinct variation in transition line broadening, dephasing time and spatial extension of the wavefunction. The fundamental Bloch-oscillating transport in a periodic structure is drastically modified and exhibits a strong damping with a surprising revival of polarization coherence which reappears on a picosecond scale.

The pulsed output from a Bose-Einstein condensate can be described using ordinary one-particle quantum mechanics. The initial state is described in terms of Stark resonances truncated in momentum space. The states obtained in this way resemble the normalizable scattering states defined in terms of Moshinsky functions. The validity of this approach and the influence of the initial population on the pulse formation is discussed. Finally, we describe an experimental setup to manufacture and observe pulsed output in Wannier-Stark systems.

The quantum and classical dynamics in a two-dimensional (2D) periodic potential influenced by a constant force is discussed and compared. Classically, the dynamics is chaotic. A branched flow of the particles similar but more structured than the coherent branched flow in a 2D electron gas is observed. In the classical case, the formation of separate decay channels is explained by dynamical trapping. The quantum dynamics closely follows the classical one.

An extremely simple and convenient method is presented for computing eigenvalues in quantum mechanics by representing position and momentum operators in matrix form. The simplicity and success of the method is illustrated by numerical results concerning eigenvalues of bound systems and resonances for Hermitian and non-Hermitian Hamiltonians as well as driven quantum systems. Various MATLAB program codes are listed.

In this work, we discuss the resonance states of a quantum particle in a periodic potential plus a static force. Originally this problem was formulated for a crystal electron subject to a static electric field and it is nowadays known as the Wannier-Stark problem. We describe a novel approach to the Wannier-Stark problem developed in recent years. This approach allows to compute the complex energy spectrum of a Wannier-Stark system as the poles of a rigorously constructed scattering matrix and solves the Wannier-Stark problem without any approximation. The suggested method is very efficient from the numerical point of view and has proven to be a powerful analytic tool for Wannier-Stark resonances appearing in different physical systems such as optical lattices or semiconductor superlattices. Comment: 94 pages, 41 figures, typos corrected, references added

In this work, we discuss the resonance states of a quantum particle in a periodic potential plus a static force. Originally this problem was formulated for a crystal electron subject to a static electric field and it is nowadays known as the Wannier-Stark problem. We describe a novel approach to the Wannier-Stark problem developed in recent years. This approach allows to compute the complex energy spectrum of a Wannier-Stark system as the poles of a rigorously constructed scattering matrix and solves the Wannier-Stark problem without any approximation. The suggested method is very efficient from the numerical point of view and has proven to be a powerful analytic tool for Wannier-Stark resonances appearing in different physical systems such as optical lattices or semiconductor superlattices.

Here we show that using Galilean transformations the non-Hermitian delocalization phenomenon, which is relevant in different fields, such as bacteria population (e.g., Bacillus subtilis), vortex pinning in superconductors, and stability solutions of hydrodynamical problems discovered by Hatano and Nelson [Phys. Rev. Lett. 77, 5706 (1996)], can be obtained from solutions of the time-dependent Schrödinger equation with a Hermitian Hamiltonian. Using our approach, one avoids the numerical complications and instabilities which result form the calculations of left and right eigenfunctions of the non-Hermitian Hamiltonian which are associated with the non-Hermitian delocalization phenomenon. One also avoids the need to replace the non-Hermitian Hamiltonian H by a supermatrix with twice the dimension of H, where the complex frequencies serve as variational parameters rather than eigenvalues of H.

A simple method of calculating the Wannier-Stark resonances in 2D lattices is suggested. Using this method we calculate the complex Wannier-Stark spectrum for a nonseparable 2D potential realized in optical lattices and analyze its general structure. The dependence of the lifetime of Wannier-Stark states on the direction of the static field (relative to the crystallographic axis of the lattice) is briefly discussed.

Summary form only given. The electronic structure of a periodic potential under a static electric field is of high interest due to its basic importance for carrier transport in solids. For obtaining a complete picture of the spectrum over the whole field range, the fundamental process of Zener tunneling to higher bands needs to be understood. Although this effect is used since decades in devices, very little is known, e.g., about its dynamics as a function of bias field. We present here a comparative experimental and theoretical study which investigates the dynamics of Zener tunneling and shows that the widely used Zener equation needs to be extended qualitatively to describe experiment. We have investigated a shallow 76/39 Å GaAs/Al0.08Ga0.92As superlattice which has one below-barrier electron miniband only.

A simple method of calculating the Wannier-Stark resonances in 2D lattices is suggested. Using this method we calculate the complex Wannier-Stark spectrum for a non-separable 2D potential realized in optical lattices and analyze its general structure. The dependence of the lifetime of Wannier-Stark states on the direction of the static field (relative to the crystallographic axis of the lattice) is briefly discussed.