How to steer properties of quantum systems by light or time-dependent perturbations has been object of investigation since the early days of quantum mechanics. Nowadays though, the rapid development in optical and microwave techniques has fueled renewed interest in this rapidly growing research field.?? In our research we focus on strongly driven quantum systems, whose properties can be shaped by intense time-dependent external perturbations. Pathways to manipulate properties of quantum matter by a time-periodic drive are often dubbed as Floquet-engineering.? Exemplarily, tunneling can be brought to a complete standstill due to destructive interference between a tunneling two-level particle and the photons of the radiation filed, a phenomenon known as coherent destruction of tunneling (CDT). Also, Floquet band-engineering can favor novel states of matter, e.g. the occurrence of a topological phase transition in an otherwise conventional superconductors. Finally, a time-dependent drive, e.g. a time-dependent bias voltage can be used to gain important information on the properties of the system of interest. An example here are missing Shapiro steps in a microwave irradiated topological Josephson junction.?
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