My current research interests revolve around quantum control and applications of quantum information theory to quantum many-body systems. In quantum control we aim to steer the dynamics of quantum systems in a desired way, which is crucial for the realization of quantum technologies. In particular, I am interested in the preparation and manipulation of topological states of matter, which are characterized by non-local properties and are thus very robust. On the other hand, quantum information theory provides a powerful toolbox to study quantum many-body systems by providing a system-independent language to describe and quantify quantum correlations. This is inspired by an earlier work on the use of classical information theory to develop algorithms for statistical physics. However, in the quantum setting, there are still many open questions on what kind of information about the system is accessible through quantum information measures and how to extract it in practice.
I have also done extensive work on hyperbolic lattices, which are lattices in negatively curved space and as such they are the analogue of periodic structures in that space. In contrast to positively curved spaces, such as the surface of a sphere, the negative counterpart cannot be completely embedded in three-dimensional space. In an experimental collaboration, we have demonstrated explicitly that hyperbolic lattices realized in metamaterials enable us to emulate the negatively curved hyperbolic space. On the theory side, we have on the one hand studied several fundamental models of topological band insulators on hyperbolic lattices and on the other hand made progress in developing the generalization of band theory to hyperbolic lattices. This progress has enabled us to study spin liquids on hyperbolic lattices, which have potential applications in quantum computing.
Previously, I have worked on topological band theory in the context of real materials (in contrast to metamaterials). I have studied various spects of multiband topology, such as momentum space degeneracies (band nodes), topological invariants and their relation to symmetries. In particular, I am interested in a multiband perspective on the above topics. This has culminated in a large project about triple (nodal) points, which are degeneracies of three bands in momentum space. We have completed the missing classification of those band nodes in the absence of spin (which applies to systems where spin-orbit interactions are negligible but also to many other systems such as photons, phonons, magnons including may metamaterials) and have found a universal higher-order bulk-boundary correspondence as well as relationships to multiband topology. For more information, check out the project description.