Floquet topological phases and skin effects in periodically driven non-Hermitian systems

We study a non-Hermitian Su-Schrieffer-Heeger model with nonreciprocal hopping under periodic driving, and show that the Floquet topological nature and non-Hermiticity can have rich interplay in this non-Hermitian Floquet topological system. We find that both the topological characteristics and the non-Hermitian skin effect are affected by the Floquet driving and can be associated with the quasienergy spectrum topology. For general choice of system and driving parameters, we derive a non-Bloch bulk-boundary correspondence to successfully describe the Floquet topological edge states with non-Hermitian skin effects. We observe interesting bipolar non-Hermitian skin effect by periodically driving the short-range non-Hermitian system, and establish its connection to the winding of Bloch quasienergy spectrum. Finally, we propose to implement the non-Hermitian quantum system with asymmetric hopping in cold atomic gases. Our work demonstrates the impact of periodic driving on non-Hermitian topological systems, and suggests a route to search for richer non-Hermitian skin effects through Floquet engineering.