Exploring new phases of effective Floquet medium
During the last decade, time-reversal and/or time-translational symmetry breaking in a driven quantum many-body system has attracted a great amount of attention. Theoretical prediction and subsequent experimental observation of new non-equilibrium phases of matter, such as time crystals and Floquet quantum Hall states, were sufficient to justify all the hype. In line with this effort, classical emulation of time-Floquet matter has emerged as one of the most immediate challenges in the fields of photonics, electromagnetics, acoustics, and phononics. This classical emulation could provide an even larger interesting playground, in which exotic quantum behaviour can be predicted and reproduced with much more controllable degrees of freedom. In this project, we plan to emulate photonic time-Floquet media in the microwave regime and experimentally reveal exceptional non-Hermitian phase transitions. For this purpose, we extend the conventional Bloch-Floquet band framework to complex-valued energy-momentum space and probe the topology in a newly introduced complex Brillouin zone.