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

• URL: http://arxiv.org/abs/2301.06255v1
• Date: Mon, 16 Jan 2023 04:30:06 GMT
• Title: Stability of time-periodic $\mathcal{PT}$ and anti-$\mathcal{PT}$-symmetric Hamiltonians with different periodicities
• Authors: Julia Cen, Yogesh N. Joglekar, Avadh Saxena
• Abstract summary: Hermitian Hamiltonians with time-periodic coefficients can be analyzed via Floquet theory. Time-periodicity offers avenues to engineer the landscape of Floquet quasi-energies across the complex plane.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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