Optical microcavities as quantum-chaotic model systems: Openness makes the difference!

Optical microcavities are open billiards for light in which electromagnetic waves can, however, be confined by total internal reflection at dielectric boundaries. These resonators enrich the class of model systems in the field of quantum chaos and are an ideal testing ground for the correspondence of ray and wave dynamics that, typically, is taken for granted. Using phase-space methods we show that this assumption has to be corrected towards the long-wavelength limit. Generalizing the concept of Husimi functions to dielectric interfaces, we find that curved interfaces require a semiclassical correction of Fresnel's law due to an interference effect called Goos-Haenchen shift. It is accompanied by the so-called Fresnel filtering which, in turn, corrects Snell's law. These two contributions are especially important near the critical angle. They are of similar magnitude and correspond to ray displacements in independent phase-space directions that can be incorporated in an adjusted reflection law. We show that deviations from ray-wave correspondence can be straightforwardly understood with the resulting adjusted reflection law and discuss its consequences for the phase-space dynamics in optical billiards.Comment: 12 pages, 5 figures, to appear in Adv. Sol. St. Phys. 4

Anderson orthogonality catastrophe in realistic quantum dots

We study Anderson orthogonality catastrophe (AOC) for an parabolic quantum dot (PQD), one of the experimentally realizable few-electron systems. The finite number of electrons in PQD causes AOC to be incomplete, with a broad distribution of many-body overlaps. This is a signature of mesoscopic fluctuations and is in agreement with earlier results obtained for chaotic quantum dots. Here, we focus on the effects of degeneracies in PQDs, realized through their inherent shell structures, on AOC. We find rich and interesting behaviours as a function of the strength and position of the perturbation, the system size, and the applied magnetic field. In particular, even for weak perturbations, we observe a pronounced AOC which is related to the degeneracy of energy levels. Most importantly, the power law decay of the many-body overlap as a function of increasing number of particles is modified in comparison to the metallic case due to rearrangements of energy levels in different shells.Comment: 14 pages, 15 figure

The optical M\"{o}bius strip cavity: Tailoring geometric phases and far fields

The M\"{o}bius strip, a long sheet of paper whose ends are glued together after a $180^{\circ}$ twist, has remarkable geometric and topological properties. Here, we consider dielectric M\"{o}bius strips of finite width and investigate the interplay between geometric properties and resonant light propagation. We show how the polarization dynamics of the electromagnetic wave depends on the topological properties, and demonstrate how the geometric phase can be manipulated between $0$ and $\pi$ through the system geometry. The loss of the M\"{o}bius character in thick cavities and for small twist segment lengths allows one to manipulate the polarization dynamics and the far-field emission, and opens the venue for applications.Comment: 6 pages, 5 figure

Multiple beam interference in a quadrupolar glass fiber

Motivated by the recent observation of periodic filter characteristics of an oval-shaped micro-cavity, we study the possible interference of multiple beams in the far field of a laser-illuminated quadrupolar glass fiber. From numerical ray-tracing simulations of the experimental situation we obtain the interference-relevant length-difference spectrum and compare it with data extracted from the experimental filter results. Our analysis reveals that different polygonal cavity modes being refractively output-coupled in the high-curvature region of the fiber contribute to the observed far-field interference.Comment: 4 pages, 4 fig

Many-body effects in the mesoscopic x-ray edge problem

Many-body phenomena, a key interest in the investigation of bulk solid state systems, are studied here in the context of the x-ray edge problem for mesoscopic systems. We investigate the many-body effects associated with the sudden perturbation following the x-ray excitation of a core electron into the conduction band. For small systems with dimensions at the nanoscale we find considerable deviations from the well-understood metallic case where Anderson orthogonality catastrophe and the Mahan-Nozieres-DeDominicis response cause characteristic deviations of the photoabsorption cross section from the naive expectation. Whereas the K-edge is typically rounded in metallic systems, we find a slightly peaked K-edge in generic mesoscopic systems with chaotic-coherent electron dynamics. Thus the behavior of the photoabsorption cross section at threshold depends on the system size and is different for the metallic and the mesoscopic case.Comment: 9 pages, 3 figures, Proceedings ``Quantum Mechanics and Chaos'' (Osaka 2006

Photoabsorption spectra and the X-ray edge problem in graphene

We study the photoabsorption cross section and Fermi-edge singularities (FES) in graphene. For fillings below one half, we find, besides the expected FES in form of a peaked edge at the threshold (Fermi) energy, a second singularity to arise at excitation energies that correspond to the Dirac point in the density of states. We can explain this behaviour by comparing our results with the photoabsorption cross section of a metal with a small central band gap where we find a very similar signature. The existence of the second singularity might prove useful for an experimental determination of the Dirac point. We also demonstrate that the photoabsorption signal is enhanced by the zigzag edge states due to their metallic-like character. Since the presence of the edge states indicates a topological defect at the boundary, our study gives an example for a Fermi-edge singularity in a system with a topologically nontrivial electronic spectrum.Comment: accepted for publication in Europhysics Letters (2011