Connecting active and passive $\mathcal{PT}$-symmetric Floquet modulation models

TL;DR

This paper introduces a unified model connecting static, Floquet, and neutral $ ext{PT}$-symmetric Hamiltonians, revealing how periodic driving influences the $ ext{PT}$-symmetry breaking transition and phase stability.

Contribution

It provides an analytical and numerical analysis of a simple time-dependent $ ext{PT}$-symmetric model that smoothly interpolates between different regimes, uncovering new $ ext{PT}$-broken phase regions.

Findings

$ ext{PT}$-broken phases extend into low and high non-Hermiticity regions.

Periodic driving alters the $ ext{PT}$-symmetry breaking threshold.

Unified model links static, Floquet, and neutral $ ext{PT}$-symmetric systems.

Abstract

Open systems with gain, loss, or both, described by non-Hermitian Hamiltonians, have been a research frontier for the past decade. In particular, such Hamiltonians which possess parity-time ($\mathcal{PT}$) symmetry feature dynamically stable regimes of unbroken symmetry with completely real eigenspectra that are rendered into complex conjugate pairs as the strength of the non-Hermiticity increases. By subjecting a $\mathcal{PT}$-symmetric system to a periodic (Floquet) driving, the regime of dynamical stability can be dramatically affected, leading to a frequency-dependent threshold for the $\mathcal{PT}$-symmetry breaking transition. We present a simple model of a time-dependent $\mathcal{PT}$-symmetric Hamiltonian which smoothly connects the static case, a $\mathcal{PT}$-symmetric Floquet case, and a neutral-$\mathcal{PT}$-symmetric case. We analytically and numerically analyze the $\mathcal{PT}$ phase diagrams in each case, and show that slivers of $\mathcal{PT}$-broken ($\mathcal{PT}$-symmetric) phase extend deep into the nominally low (high) non-Hermiticity region.