{
  "id": "oai:papers.qnfo.org:4d-harper-hofstadter-zero-modes-in-synthetic-frequency-microring-lattices",
  "slug": "4d-harper-hofstadter-zero-modes-in-synthetic-frequency-microring-lattices",
  "title": "4D Harper‑Hofstadter Zero‑Modes in Synthetic‑Frequency Microring Lattices",
  "authors": [
    "Rowan Brad Quni-Gudzinas"
  ],
  "abstract": "Synthetic‑frequency dimensions enable on‑chip frequency‑comb transport that is immune to scattering loss, but experimental demonstrations have been limited to one‑dimensional lattices. We fill this gap by analytically mapping a driven 10 × 10 microring array onto a four‑dimensional Harper‑Hofstadter Hamiltonian. Using the ultra‑high quality factor Q≈10¹0 reported in [1] and a terahertz electro‑optic drive field E_THz=10⁷V m^-1 (as analyzed in [13]), we obtain a cavity linewidth κ/2π≈19.4kHz, a photon lifetime τ≈8.22 mus, and a synthetic hopping rate J≈36.06GHz. The resulting hopping‑to‑loss ratio J/κ≈1.86×10⁶ places the system deep in the tight‑binding regime. At an operating temperature of 80 K the thermal occupation of the 3.5 THz drive band is n=0.1396, yielding an effective per‑hop error probability p_eff=1.4×10^-4 and a transport fidelity F₁00=0.986 over 100 synthetic hops. A projection of the required terahertz source power is 12.5W. These results demonstrate that geometric protection of a chiral zero‑mode is achievable with realistic device parameters, providing a concrete target for fault‑tolerant photonic processors.",
  "abstract_markdown": "Synthetic‑frequency dimensions enable on‑chip frequency‑comb transport that is immune to scattering loss, but experimental demonstrations have been limited to one‑dimensional lattices. We fill this gap by analytically mapping a driven 10 × 10 microring array onto a four‑dimensional Harper‑Hofstadter Hamiltonian. Using the ultra‑high quality factor $Q\\approx10^{10}$ reported in [1] and a terahertz electro‑optic drive field $E_{\\text{THz}}=10^{7}\\,$V m\\(^{-1}\\) (as analyzed in [13]), we obtain a cavity linewidth $\\kappa/2\\pi\\approx19.4\\,$kHz, a photon lifetime $\\tau\\approx8.22\\;\\mu\\text{s}$, and a synthetic hopping rate $J\\approx36.06\\,$GHz. The resulting hopping‑to‑loss ratio $J/\\kappa\\approx1.86\\times10^{6}$ places the system deep in the tight‑binding regime. At an operating temperature of 80 K the thermal occupation of the 3.5 THz drive band is $n=0.1396$, yielding an effective per‑hop error probability $p_{\\text{eff}}=1.4\\times10^{-4}$ and a transport fidelity $F_{100}=0.986$ over 100 synthetic hops. A projection of the required terahertz source power is $12.5\\,$W. These results demonstrate that geometric protection of a chiral zero‑mode is achievable with realistic device parameters, providing a concrete target for fault‑tolerant photonic processors.",
  "date": "2026-10-26",
  "first_published": "2026-10-26",
  "last_revised": "2026-10-26T00:00:00Z",
  "modified": "2026-10-26T00:00:00Z",
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  "language": "en",
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    "versioned research publication"
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  "quality_label": "High-quality scholarly research",
  "quality_basis": "QNFO publisher classification for open-access, versioned research with a public revision history and reader correction channel; this is not a claim of independent peer review.",
  "quality_evidence_url": "https://qnfo.org/about",
  "peer_review_status": "Not independently peer-reviewed",
  "resource_type": "ScholarlyArticle",
  "doi": null,
  "doi_url": null,
  "url": "https://papers.qnfo.org/papers/4d-harper-hofstadter-zero-modes-in-synthetic-frequency-microring-lattices",
  "license_url": "https://legal.qnfo.org/",
  "license_spdx": null,
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    "creators": [
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        "name": "Rowan Brad Quni-Gudzinas",
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    "titles": [
      {
        "title": "4D Harper‑Hofstadter Zero‑Modes in Synthetic‑Frequency Microring Lattices"
      }
    ],
    "publisher": "QNFO",
    "publicationYear": "2026",
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    "dates": [
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        "date": "2026-10-26",
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        "date": "2026-10-26",
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        "description": "Synthetic‑frequency dimensions enable on‑chip frequency‑comb transport that is immune to scattering loss, but experimental demonstrations have been limited to one‑dimensional lattices. We fill this gap by analytically mapping a driven 10 × 10 microring array onto a four‑dimensional Harper‑Hofstadter Hamiltonian. Using the ultra‑high quality factor Q≈10¹0 reported in [1] and a terahertz electro‑optic drive field E_THz=10⁷V m^-1 (as analyzed in [13]), we obtain a cavity linewidth κ/2π≈19.4kHz, a photon lifetime τ≈8.22 mus, and a synthetic hopping rate J≈36.06GHz. The resulting hopping‑to‑loss ratio J/κ≈1.86×10⁶ places the system deep in the tight‑binding regime. At an operating temperature of 80 K the thermal occupation of the 3.5 THz drive band is n=0.1396, yielding an effective per‑hop error probability p_eff=1.4×10^-4 and a transport fidelity F₁00=0.986 over 100 synthetic hops. A projection of the required terahertz source power is 12.5W. These results demonstrate that geometric protection of a chiral zero‑mode is achievable with realistic device parameters, providing a concrete target for fault‑tolerant photonic processors.",
        "descriptionType": "Abstract"
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        "description": "Publisher quality classification: High-quality scholarly research. QNFO publisher classification for open-access, versioned research with a public revision history and reader correction channel; this is not a claim of independent peer review.",
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