R. Grobe

A split-domain algorithm for time-dependent multi-electron wave functions

A computational technique for studying the time-development of two-electron systems is presented, with particular attention given to photoionization or photodetachment of two-electron, one-dimensional model atoms. The technique is based on a partitioning of the spatial wave function into inner and outer parts. The electron-electron interaction is fully accounted for in the inner part, but neglected in the outer part, where the electrons are typically far apart. The time development of the inner part is calculated using a full numerical grid, but the time-development of the outer part is accomplished using canonical basis states. The use of canonical basis states allows the study of atom-laser dynamics for much longer laser pulse durations and lower laser frequencies than would be possible using standard grid techniques.

Atoms in strong laser fields: challenges in relativistic quantum mechanics

We address the challenges raised by the question of how to produce quantitative data in order to reproduce and to interpret the results of recent and future experiments performed with ultra-intense laser pulses. The main challenges lie in the problem of implementing reliable numerical codes for describing quantum processes experienced by electrons brought in the relativistic regime in the presence of the field.

Two-mode SU(2) and SU(1,1) Schrödinger cat states

Abstract We study the non-classical properties of Schrodinger cat states given as superpositions of two-mode SU(1, 1) and SU(2) coherent states. The SU(1, 1) and SU(2) coherent states themselves have strong non-classical properties and we find that these properties are enhanced at least for some superpositions. We propose a method of generating such states in the context of cavity quantum electrodynamics.

What is the relativistic spin operator

Although the spin is regarded as a fundamental property of the electron, there is no universally accepted spin operator within the framework of relativistic quantum mechanics. We investigate the properties of different proposals for a relativistic spin operator. It is shown that most candidates are lacking essential features of proper angular momentum operators, leading to spurious zitterbewegung (quivering motion) or violation of the angular momentum algebra. Only the Foldy–Wouthuysen operator and the Pryce operator qualify as proper relativistic spin operators. We demonstrate that ground states of highly charged hydrogen-like ions can be utilized to identify a legitimate relativistic spin operator experimentally.

Entanglement for pair production on the zeptosecond scale

We analyse the degree of two-particle entanglement between an electron and a positron that are created in vacuum in the presence of a supercritical field. This degree of entanglement is determined from the spatially and temporally resolved two-particle wave function calculated from relativistic quantum field theory. Some spin components of the two particles are fully correlated with respect to a simultaneous measurement. However, the positions where the two particles are created by the field can be apart from each other by as much as the Compton wavelength for an extended supercritical field. We calculate the K parameter from the two-particle wave function as a quantitative measure for the degree of entanglement.

Relativistic suppression of wave packet spreading

We investigate numerically the solution of Dirac equation and analytically the Klein-Gordon equation and discuss the relativistic motion of an electron wave packet in the presence of an intense static electric field. In contrast to the predictions of the (non-relativistic) Schroedinger theory, the spreading rate in the fields polarization direction as well as in the transverse directions is reduced.

Relativistic spin operators in various electromagnetic environments

Different operators have been suggested in the literature to describe the electrons spin degree of freedom within the relativistic Dirac theory. We compare concrete predictions of the various proposed relativistic spin operators in different physical situations. In particular, we investigate the so-called Pauli, Foldy-Wouthuysen, Czachor, Frenkel, Chakrabarti, Pryce, and Fradkin-Good spin operators. We demonstrate that when a quantum system interacts with electromagnetic potentials the various spin operators predict different expectation values. This is explicitly illustrated for the scattering dynamics at a potential step and in a standing laser field and also for energy eigenstates of hydrogenic ions. Therefore, one may distinguish between the proposed relativistic spin operators experimentally.

Introductory review on quantum field theory with space–time resolution

We review the steps needed to reduce quantum field theory to quantum mechanics as its limiting case. While processes involving a changing number of particles require a quantum field theoretical description, some works used quantum mechanical data based on the single particle Dirac equation to predict the outcome. These non-quantum field theoretical approaches have led to conceptual controversies that are often related to the negative energy states, which are characteristic of the Dirac equation. As a result, the issues about the physical reality of the relativistic localisation phenomenon, the Zitterbewegung and the Klein paradox are widely discussed in many textbooks. In order to contribute to this discussion, we review recent computer simulations of oversimplified model systems based on quantum field theory. The direct visualisation of intrinsically quantum field theoretical process with full spatial and temporal resolutions can provide us with some first insight into the spontaneous electron–positron pair creation from the vacuum triggered by a strong external (supercritical) force field and with the resolution of the Klein paradox.

Impact of large-angle scattering on diffusively backscattered halos

We discuss the impact of large-angle scattering events in highly forward-scattering media on the spatial distribution of the diffusively reflected light. We show that, even for highly forward-scattering media, the reflected light near the incident beam axis is strongly dependent on the small number of large-angle scattering events. Reliable modeling of near-axis reflection thus requires accurate knowledge of the scattering phase functions behavior at large angles.

Scaling of light scattering with density of scatterers

We inject a laser beam into a tank filled with a milk-water emulsion and measure the intensity distribution of the scattered light. As we change the concentration of the milk, we observe a nontrivial change in the light intensity as a function of the detector position. We analyze the light on and parallel to the input beam direction, as well as the scattered light in the transverse direction. The nonmonotonic scaling of the intensity as a function of the concentration and the position is also predicted by Monte Carlo simulations. With a doubling of the concentration, the detected light along the optical axis decreases globally, whereas the reflected light decreases or increases depending on the location of the detector.