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We introduce the notion of adiabatic state-flip of a Floquet Hamiltonianassociated with a non-Hermitian system that it is subjected to two drivingschemes with clear separation of time scales. The fast (Floquet) modulationscheme is utilized to re-allocate the exceptional points in the parameter spaceof the system and re-define the topological features of an adiabatic cyclicmodulation associated with the slow driving scheme. Such topologicalre-organization can be used in order to control the adiabatic transport betweentwo eigenmodes of the Floquet Hamiltonian. The proposed scheme provides adegree of reconfigurability of adiabatic state transfer which can findapplications in system control in photonics and microwave domains.

Floquet Protocols of Adiabatic State-Flips and Re-Allocation of Exceptional Points