Non-Floquet engineering in periodically driven non-Hermitian systems

TL;DR

This paper introduces a non-Floquet approach to analyze topological phases in periodically driven non-Hermitian systems, overcoming limitations of traditional Floquet theory in dissipative quantum environments.

Contribution

It proposes a novel non-Floquet framework for characterizing topological phases in non-Hermitian systems, revealing localization behaviors and enabling new topological material designs.

Findings

Eigenstates exhibit Wannier-Stark localization in frequency space.

Choice of driving period start point affects localization behavior.

Method can be used to design detectors for quantum phases.

Abstract

Floquet engineering, modulating quantum systems in a time periodic way, lies at the central part for realizing novel topological dynamical states. Thanks to the Floquet engineering, various new realms on experimentally simulating topological materials have emerged. Conventional Floquet engineering, however, only applies to time periodic non-dissipative Hermitian systems, and for the quantum systems in reality, non-Hermitian process with dissipation usually occurs. So far, it remains unclear how to characterize topological phases of periodically driven non-Hermitian systems via the frequency space Floquet Hamiltonian. Here, we propose the non-Floquet theory to identify different Floquet topological phases of time periodic non-Hermitian systems via the generation of Floquet band gaps in frequency space. In non-Floquet theory, the eigenstates of non-Hermitian Floquet Hamiltonian are temporally deformed to be of Wannier-Stark localization. Remarkably, we show that different choices of starting points of driving period can result to different localization behavior, which effect can reversely be utilized to design detectors of quantum phases in dissipative oscillating fields. Our protocols establish a fundamental rule for describing topological features in non-Hermitian dynamical systems and can find its applications to construct new types of Floquet topological materials.