Usually, the counter-intuitive quantum mechanical behavior of matter is confined to the microscopic world of atoms. However, under certain circumstances quantum behavior can be transferred from the (sub)atomic scale to the macroscopic scale. Prime examples of this are superconductors and superfluids, which exhibit flow without friction or losses. This offers a unique possibility to probe quantum mechanics, not by zooming in on the very small length scales with a microscope or a particle accelerator, but by bringing out the quantum nature to the scale of everyday objects. And that, in a nutshell, is the core research topic for our research group, “Theory of Quantum Systems and Complex Systems” (TQC). Put in more technical terms: we focus on the quantum theory of many-body systems, and our method of choice is path integration.
There are several specific areas where we look for quantum behavior:
- In solids: We investigate mechanisms for superconductivity (the quest for high-Tc superconductors) and we model how superconducting properties can be modified by nanopatterning. We also look at collective excitations of electrons – plasmonics – and the interplay of light and metallic nanoparticles, quantum dots, and systems with reduced dimensionality. Other playgrounds to investigate the many-electron system are helium, where we have looked both at multielectron bubbles and at electrons on helium, and semiconductor devices.
- In atomic gases: Here, we focus on superfluidity and Bose-Einstein condensation in ultracold atomic gases, both bosonic and fermionic. The adjustability of the interatomic interaction strength, the possibility to build artificial gauge fields into the effective Hamiltonians, and the versatility of the confinement geometry (such as an optical lattice) are all used to study fermion pairing and superfluid properties in regimes and under conditions hitherto inaccessible in solids.
- In condensed light: Photons in a cavity can be hybridized with excitons, and form polaritons, resulting in a fluid of interacting photons with a small effective mass. In the appropriate regime of temperatures and density, this also becomes a superfluid. Whereas the atomic gases provide superfluids that are mostly in equilibrium, the photonic superfluid is an out-of-equilibrium system which opens the way to study out-of-equilibrium thermodynamics and turbulence.
A favored theoretical instrument to describe the quantum fluids, is Feynman's path integral theory. We contribute to the development and refinement of this method, for example relating to Wigner function propagators and a truncated Wigner variational method. The development of the mathematical framework of the theory has led to "spin-off" topics, related to econophysics. Exotic Lagrangians can be used to price exotic financial instruments using path-integration. This constitutes a line of research by itself: the study of complex systems using path integrals.