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

## TL;DR

This paper explores non-Hermitian Floquet topological phases in a double kicked rotor system, revealing new topological states characterized by winding numbers and demonstrating their detection and correspondence with edge states.

## Contribution

It introduces a non-Hermitian extension of the double kicked rotor model, characterizes new Floquet topological phases, and establishes their bulk-edge correspondence.

## Key findings

- Identification of various non-Hermitian Floquet topological phases
- Introduction of a generalized mean chiral displacement for detection
- Mapping to a lattice model revealing topological edge states

## Abstract

Dynamical kicking systems possess rich topological structures. In this work, we study Floquet states of matter in a non-Hermitian extension of double kicked rotor model. Under the on-resonance condition, we find various non-Hermitian Floquet topological phases, with 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 uncover the richness of Floquet topological states in non-Hermitian dynamical kicking systems.