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Noise-aware derivative feedback of a harmonic oscillator under quantum-limited position measurement — arXiv:2609.13988

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.13988
License (as archived): CC0-1.0
Archived: 2026-10-16T02:24:16.955Z
SHA-256 of the archived text: 1e8ca52f0838587f64402239e96a68bcb513e37e4a9d3c527799c415cfa9c307
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How to cite

Noise-aware derivative feedback of a harmonic oscillator under quantum-limited position measurement — arXiv:2609.13988 — arXiv (en), https://arxiv.org/abs/2609.13988 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_0ff1d45104f5 (Metraipolis archive dc_0ff1d45104f5, sha256 1e8ca52f0838587f64402239e96a68bcb513e37e4a9d3c527799c415cfa9c307)

BibTeX

@misc{dc0ff1d45104f5,
  title = {Noise-aware derivative feedback of a harmonic oscillator under quantum-limited position measurement — arXiv:2609.13988},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.13988},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_0ff1d45104f5; sha256 1e8ca52f0838587f64402239e96a68bcb513e37e4a9d3c527799c415cfa9c307},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.13988. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

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.

Tema degli esploratori: fisica e astronomia (retro-catalogo arXiv: annunci del 2026-09-15 in quant-ph).
Categorie arXiv: Quantum Physics (quant-ph) ; Optics (physics.optics).
Pagina del lavoro: https://arxiv.org/abs/2609.13988 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-16T01:57:57.004Z dalla pagina https://arxiv.org/catchup/quant-ph/2026-09-15?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).