{
  "abstract": "We study measurement-based feedback control of a damped harmonic oscillator, motivated by optomechanical and interferometric position measurements, in which feedback is synthesized from a displacement measurement. For a band-limited derivative controller, the loop shapes the mechanical susceptibility and reinjects measurement noise, creating a tradeoff between stabilization and noise amplification. We present a compact classical formulation that isolates this tradeoff in the closed-loop displacement spectrum and identifies the parameters governing resonance suppression versus noise-driven actuation. We then extend the same topology to a quantum-limited position detector, enforcing the imprecision-backaction constraint and introducing finite measurement bandwidth that regularizes high-frequency noise reinjection and adds phase lag in the feedback path. In the high-$Q$ regime we obtain an analytic design rule for the optimal feedback gain at fixed controller and measurement bandwidths and compare it with full-spectrum calculations. The comparison shows that a high mechanical quality factor alone does not guarantee quantitative agreement: the accuracy of the near-resonant approximation depends strongly on the controller and measurement bandwidths. Because finite measurement bandwidth changes both the magnitude and phase of the feedback loop, the analysis separates the near-resonant damping contribution from imprecision-noise reinjection and shows that positive near-resonant feedback damping requires the product of the controller cutoff and measurement bandwidth to exceed the square of the mechanical resonance frequency. Finally, we present a dimensionless map of the gain-optimized high-$Q$ occupation and compare its predictions with full-spectrum optimization. All analytical gains evaluated in this map satisfy the full closed-loop stability criterion for these parameters.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": "Journal reference: Eur. Phys. J. D 80, 156 (2026)",
  "arxiv": "2609.13988",
  "author_total": 1,
  "authors": [
    {
      "name": "Vedran Vujnović"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/e3syftehgzkan.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.13988",
  "fulltext_url": null,
  "id": "e3syftehgzkan",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.13988",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "physics.optics"
    ],
    [
      "arxiv",
      "quant-ph"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2609.13988",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-12",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/e3syftehgzkan.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:06Z",
      "native_id": "2609.13988",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.13988"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:physics.optics",
      "subfield": "optics-photonics"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Noise-aware derivative feedback of a harmonic oscillator under quantum-limited position measurement",
  "title_text": "Noise-aware derivative feedback of a harmonic oscillator under quantum-limited position measurement",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:06Z",
  "url": "https://research.draconitic.com/paper/e3syftehgzkan",
  "venue": "arXiv",
  "versions": [
    {
      "doi": "10.1140/epjd/s10053-026-01271-3",
      "pid": null,
      "relation": "published-as",
      "title": null,
      "venue": null
    }
  ]
}