Many effects studied in the field of quantum matter are of great conceptual value but hard to find realized in nature. In turn, some of these effects are not as intrinsically ‘quantum’ as they may seem at first sight. For instance, the Berry phase, responsible for many phenomena that have been in the focus of recent research, is also present in classical physics. For such phenomena, classical systems, over which we can have a much higher level of control, provide a viable route to realize experimentally effects inspired from quantum condensed matter physics.
A platform we work on in our group are electrical circuits. They emulate lattice models and topological band structures in the form of a periodic arrangement of resistors, capacitors, inductors and possibly more ‘exotic’ circuit elements. The resulting electrical circuits allow to realize, in a very controlled manner, lattice models with hermitian and non-hermitian couplings, can be operated in a linear or non-linear regime, and be tailored to be reciprocal or not. The circuits can also be driven to emulate Floquet dynamics. In addition, local as well as non-local couplings may be implemented, which in particular enables the study of different boundary conditions. Detailed measurements allow a complete determination of the spectrum and the eigenmodes of such a circuit and thus an unprecedented level of access for physical systems.
Non-Hermitian quantum systems
One of the first lessons we learn in quantum mechanics is that Hamiltonians are Hermitian operators. The dynamics or response of open quantum systems, however, is often described by local non-Hermitian operators. In comparison to Hermitian operators, they may have drastically different properties with regards to their spectral stability against perturbations and their topology. For instance, non-Hermitian systems may show a skin effect, leading to ta localization of all eigenmodes toward the boundary. Novel topological phases include the exceptional topological insulator, as well as complex band structures with exceptional point degeneracies. We explore these effects by studying quantum or classical systems with loss and gain
Thermalization and Dynamics of Quantum Systems
The theory of quantum statistical mechanics dictates the generic behavior of quantum systems with many degrees of freedom, from a gas all the way to a magnet. It rests on the eigenstate thermalization hypothesis which states that locally, an eigenstate of a system looks like a thermal state with the eigenstate's energy density. Consequently, any local information imprinted on a system at some initial time will be lost.
Specific quantum mechanical systems, which violate eigenstate thermalization in more or less severe ways, are a current research frontier that challenges our fundamental intuition about statistical physics. Systems which exhibit a phenomenon called many-body localization, for example, violate eigenstate thermalization violently and keep a memory of their initial state for (theoretically) infinitely long time. In contrast, systems with so-called scar states in their spectrum show a similar phenomenon when initialized in some specific form. We explore these and related phenomena with a range of theoretical tools, including numerical tensor network calculations and of toy models amenable to analytical solutions.
More broadly, we are interested in dynamical behavior of interacting open quantum systems, which give rise to intriguing phenomena beyond “classical wisdom”.