Stability of time-periodic $\mathcal{PT}$ and anti-$\mathcal{PT}$-symmetric Hamiltonians with different periodicities

TL;DR

This paper explores the stability and phase structure of two-level non-Hermitian Hamiltonians with different periodicities using Floquet theory, revealing complex landscapes of stable and unstable regions.

Contribution

It provides a detailed analysis of stability regions and exceptional points in non-Hermitian Hamiltonians with varying periodicities, extending Floquet theory applications.

Findings

Identification of stability regions with real Floquet quasi-energies.

Mapping of exceptional point degeneracies in parameter space.

Discovery of rich phase structures in time-periodic non-Hermitian systems.

Abstract

Hermitian Hamiltonians with time-periodic coefficients can be analyzed via Floquet theory, and have been extensively used for engineering Floquet Hamiltonians in standard quantum simulators. Generalized to non-Hermitian Hamiltonians, time-periodicity offers avenues to engineer the landscape of Floquet quasi-energies across the complex plane. We investigate two-level non-Hermitian Hamiltonians with coefficients that have different periodicities using Floquet theory. By analytical and numerical calculations, we obtain their regions of stability, defined by real Floquet quasi-energies, and contours of exceptional point (EP) degeneracies. We extend our analysis to study the phases that accompany the cyclic changes. Our results demonstrate that time-periodic, non-Hermitian Hamiltonians generate a rich landscape of stable and unstable regions.