P2: Floquet engineering, dissipation, and cavities using tensor networks

• Applicant: Professor Dr. Christoph Karrasch
• Subject Area: Theoretical Condensed Matter Physics
• Term: since 2025
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 531215165

In this project, we will develop tensor network techniques to study driven systems. The aim is to explore hitherto uncharted optical control routes with direct implications for experiments. Along this way, our first objective is to theoretically investigate and describe the combined effects of periodic driving, dissipation, and interactions in one dimension from the perspective of fundamental science. We will explore to which extent dissipation can leverage detrimental heating and how new avenues for controlling phases of matter can open up at the interface of Floquet and dissipation engineering. These insights integrally contribute to the goals of OPTIMAL. First, a driven spin-model testbed will be employed. It forms a well-defined starting point where one expects that the entanglement grows only moderately, tensor networks become highly accurate and one can thus readily access its non-trivial nonequilibrium phase diagram as a function of the dissipation and driving strength. This links to fundamental, open questions relevant to the phononic and electronic, on-chip Floquet experiments, where dissipation is expected to play a key role. These experiments will start in higher than one dimension, but P6 is expected to focus also on one dimension towards the end of the first funding period, and a quantitative comparison to experiments can be made with the machinery set up in P2. We will subsequently study more complex one-dimensional models and link to our second objective, whose focus is on studying cavity as well as classical Floquet engineering in one-dimensional Mott systems such as TiOCl or CuGeO3. E.g., we will investigate how to dynamically control such systems using classical light or establish the cavity-modified phase diagram, where the experiments will provide an experimental testbed. Our third, long-term objective is to study systems strongly coupled to a bath and/or systems in two dimensions. To this end, we will bring a renormalization-group based method into play. Here, we will also attempt (challenging) tensor network studies for mixed phonon-photon systems as well as in two dimensions.

• DFG Programme: Research Units
• Subproject of: FOR 5750: Optical Control of Quantum Materials (OPTIMAL)