{
  "id": "2301.06255",
  "version": "v1",
  "published": "2023-01-16T04:30:06.000Z",
  "updated": "2023-01-16T04:30:06.000Z",
  "title": "Stability of time-periodic $\\mathcal{PT}$ and anti-$\\mathcal{PT}$-symmetric Hamiltonians with different periodicities",
  "authors": [
    "Julia Cen",
    "Yogesh N. Joglekar",
    "Avadh Saxena"
  ],
  "categories": [
    "quant-ph"
  ],
  "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-01-16T04:30:06.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "symmetric hamiltonians",
      "periodicities",
      "floquet theory",
      "real floquet quasi-energies",
      "two-level non-hermitian hamiltonians"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}