Research Interests

For the broader audience:
The group's research is on electronic and optical mesoscopic systems, i.e. on systems in between (meso) the macroscopic (classical) and microscopic (quantum mechanical) world. Their size is, as a characteristics, smaller than the decoherence length such that interference matters: Self-interference in ballistic systems makes the wavefunctions to be sensistive to the geometry of the system and very different from those of bulk samples. Interference plays also a crucial role in transport - weak localization and the Aharonov-Bohm effect a paradigms for this.
Our research has strong links to the fields of condensed matter physics and classical nonlinear dynamics. We are interested, as a first topic and in a number of projects, in many-body effects in mesoscopic systems for electrons, namely how the signatures of the Kondo effect and Fermi edge singularities differ from the bulk results, and how do they depend on the geometry of the system. This last question concerns problems addressed in the field of quantum chaos - the quantum mechanical properties of classically chaotic (as well as integrable and mixed) systems.

We investigate these issues also in a second topic that concerns optical microcavities, i.e. mesoscopic systems for light. The light is, unlike the electrons, not confined by hard walls, but rather by total internal reflection. Because of the possibility of refractive escape, those systems are intrinsically open. We are interested in how this openness affects the dynamics of the system in the ray and wave picture and find that there are considerable deviations. As an example, the reflection of light at curved interfaces in situations when the wavelength becomes comparable to the radius of curvature does not follow the usual specular reflection law. This has drastic effects for the ray-wave (classical-quantum) correspondence in those systems.

Although we do mainly basic research, there is one aspect that is of tremendous interest for application in, e.g., optoelectronics, namely to have very small lasers. As the concept of the conventional (Fabry-Perot) laser cannot be shrinked to arbitrarily small scales for practical reasons, alternatives are needed. Together with Jan Wiersig, we predicted highly directional emission form microlasers with the shape of a slightly deformed disk (the so-called Limacon shape), Phys. Rev. Lett. 100, 033901 (2008) . This idea was succesfully tested in experiments by four independent groups within the following year. We landed another breakthrough on the topic of spiral microcavities where we could identify the conditions and optimal parameters for achieving directional emission (together with Tae-Yoon Kwon, Opt. Lett. 34, 136 (2009) .

More specifically:

Projects presently under investigation

Many-body effects in the mesoscopic regime

-- Fermi-edge singularities: Anderson orthogonality catastrophe and the x-ray edge problem in chaotic and regular quantum dots and in graphene, interplay with Kondo physics, signatures of many-body effects in the photoabsorption cross section and transport quantities, Bose-Einstein condensates subject to a sudden perturbation
-- Kondo box problem: Mean-field approximation, chances and limitations
-- Graphene: Parity anomaly, Berry phases, specific signatures of Fermi-edge singularities

Quantum chaos in optical microresonators

-- Semiclassical concepts and corrections: Goos-Hänchen effect and corrections to ray optics at curved dielectric interfaces, generalisation of the concept of Husimi functions to open systems, S-matrix method for optical systems, ray-wave correspondence
-- Microlasers with directed emission and far-field characteristics of optical microcavities: Directed emission from cavities with Limacon and spiral shape, Ray picture vs. wave simulations vs. experimental results, agreement and deviations between ray and wave picture
-- Nonlinear optical transport: Similarities and differences between Kerr media and Bose Einstein condensates

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