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.

A physical system describable with a non-Hermitian Hamiltonian is characterised by the presence of exceptional points (EPs), i.e., branching point singularities at which two or more eigenstates coalesce in parameter space. These non-Hermitian degeneracies have been the center of much attention due to the associated singular eigenvalue surface topology in parameter space. However, the reduction of an eigenspace dimensionality has not been thoroughly investigated in an active metasurface platform. The experimental sectioning of a branching topology in the parameter space of a passive metasurface is a demanding task because of the repeated sample fabrications with quasi-continuously varying meta-atom designs. It is thus highly desirable to have precise real-time control on the parameters for access to the EP. The necessity of this active control justifies the integration of a precisely tunable element into the metasurface platform. For this purpose, we plan to hybridize gated graphene micro-ribbons with non-Hermitian meta-atoms and demonstrate electrically controlled sectioning of a branching topology of self-intersecting Riemann surfaces.