Non-Hermitian Floquet topological phases in the double-kicked rotor

Dynamical kicking systems possess rich topological structures. In this work we study Floquet states of matter in a non-Hermitian extension of the double-kicked rotor model. Under the on-resonance condition, we find various non-Hermitian Floquet topological phases, each being characterized by a pair of topological winding numbers. A generalized mean chiral displacement is introduced to detect these winding numbers dynamically in two symmetric time frames. Furthermore, by mapping the system to a periodically quenched lattice model, we obtain the topological edge states and unravel the bulk-edge correspondence of the non-Hermitian double-kicked rotor. These results reveal the richness of Floquet topological states in non-Hermitian dynamical kicking systems.