Time-periodic driving has become a useful tool for novel tunability in many-body systems, opening the door for new phases of effective Hamiltonians and artificial gauge fields. Theoretically and experimentally this works well at higher frequencies, but as the frequency is lowered more and more states are coupled leading to complications and heating. At the same time, the intermediate to low frequency regime also promises a very rich physics including resonances, which will be the topic of this talk.  

Floquet theory will be reviewed in detail to answer the question, if and how resonances can be treated analytically and theoretically in selected model systems. The first example involves driven Bosons in one-dimension, corresponding to a time-periodic Lieb Liniger model.  Analytical progress can be made using a Floquet-Bogoliubov rotation to obtain the Floquet eigenstates exactly and predict resonance behavior in agreement with experiments. Consequences for related systems of non-linear magnons, spin chains and Bose condensates are presented, as well as methods and challenges for possible numerical simulations.

The second example concerns resonant Floquet scattering, where the effective interaction can be tuned dramatically by using a time-periodic scattering length. In this case heating can be analyzed explicitly and recent experiments fully confirm the picture of a novel Floquet resonance.  Numerical aspects and open questions will be discussed.  

Sebastian Eggert is a distinguished professor at Technische Universität Kaiserslautern in Germany. He earned his M.Sc. in Physics (1990) from the University of Wyoming, USA, and went on to obtain his Ph.D. in Physics (1994) at University of British Columbia in Canada, working with the renowned Prof. Ian Affleck. Following his doctorate, he held a postdoctoral fellowship at Chalmers University of Technology in Sweden (1994~1996). He then served as an Assistant Professor (1994~1997) before being promoted to Associate Professor and Fellow of the Swedish Research Council (1998~2004). Since 2004, he has been a full professor at Technische Universität Kaiserslautern. His research interests focus on many-body quantum phenomena in low-dimensions, where strong correlations dominate the collective behavior and give rise to universal properties and fascinating physical phenomena. He currently explores dynamic effects in these systems. By integrating field theoretical methods with advanced numerical simulations, his works provide detailed comparisons with experimental results.