arXiv subjects

Tobias Kramer

Publications and source records attributed to Tobias Kramer.

60 records · Page 4Linked to original sources

arXiv2003

Matter waves from localized quantum sources

Matter waves originating from a localized region in space appear commonly in physics. Examples are photo-electrons, ballistic electrons in nanotechnology devices (scanning-tunneling microscopy, quantum Hall effect), or atoms released from a coherent source (atom laser). We introduce the energy-dependent Green function as a suitable tool to calculate the arising currents. For some systems experimental data is available and in excellent agreement with the presented results.

quant-ph↗

arXiv2003

Electron propagation in crossed magnetic and electric fields

Laser-atom interaction can be an efficient mechanism for the production of coherent electrons. We analyze the dynamics of monoenergetic electrons in the presence of uniform, perpendicular magnetic and electric fields. The Green function technique is used to derive analytic results for the field--induced quantum mechanical drift motion of i) single electrons and ii) a dilute Fermi gas of electrons. The method yields the drift current and, at the same time it allows us to quantitatively establish the broadening of the (magnetic) Landau levels due to the electric field: Level number k is split into k+1 sublevels that render the $k$th oscillator eigenstate in energy space. Adjacent Landau levels will overlap if the electric field exceeds a critical strength. Our observations are relevant for quantum Hall configurations whenever electric field effects should be taken into account.

quant-ph↗

arXiv2002

Ballistic matter waves with angular momentum: Exact solutions and applications

An alternative description of quantum scattering processes rests on inhomogeneous terms amended to the Schroedinger equation. We detail the structure of sources that give rise to multipole scattering waves of definite angular momentum, and introduce pointlike multipole sources as their limiting case. Partial wave theory is recovered for freely propagating particles. We obtain novel results for ballistic scattering in an external uniform force field, where we provide analytical solutions for both the scattering waves and the integrated particle flux. Our theory directly applies to p-wave photodetachment in an electric field. Furthermore, illustrating the effects of extended sources, we predict some properties of vortex-bearing atom laser beams outcoupled from a rotating Bose-Einstein condensate under the influence of gravity.

quant-ph↗

arXiv2001

Matter waves from quantum sources in a force field

Localized scattering phenomena may result in the formation of stationary matter waves originating from a compact region in physical space. Mathematically, such waves are advantageously expressed in terms of quantum sources that are introduced into the Schrödinger equation. The source formalism yields direct access to the scattering wave function, particle distribution, and total current. As an example, we study emission from three-dimensional Gaussian sources into a homogeneous force field. This model describes the behaviour of an atom laser supplied by an ideal Bose-Einstein condensate under the influence of gravity. We predict a strong dependence of the beam profile on the condensate size and the presence of interference phenomena recently observed in photodetachment experiments.

quant-ph↗

arXiv2001

Four-path interference and uncertainty principle in photodetachment microscopy

We study the quantal motion of electrons emitted by a pointlike monochromatic isotropic source into parallel uniform electric and magnetic fields. The two-path interference pattern in the emerging electron wave due to the electric force is modified by the magnetic lens effect which periodically focuses the beam into narrow filaments along the symmetry axis. There, four classical paths interfere. With increasing electron energy, the current distribution changes from a quantum regime governed by the uncertainty principle, to an intricate spatial pattern that yields to a semiclassical analysis.

quant-ph↗

arXiv1999

Exact electron states in 1D (quasi-) periodic arrays of delta-potentials

Exact one-electron eigenstates in finite parts of 1D periodic and Fibonacci chains of attractive and repulsive delta potentials are computed and analyzed. Bloch and bound state boundary conditions are related in terms of transfer matrices. Scenarios of positive and negative energy are distinguished. The dependence on the potential strength parameter is analyzed. The scattering matrix is computed. Implications for the interpretation of band germs in quasiperiodic chains are discussed.

math-ph↗