Weak-Value Amplification for Longitudinal Phase Measurements Approaching the Shot-Noise Limit Characterized by Allan Variance
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Quantum Physics arXiv:2602.17035 (quant-ph) [Submitted on 19 Feb 2026] Title:Weak-Value Amplification for Longitudinal Phase Measurements Approaching the Shot-Noise Limit Characterized by Allan Variance Authors:Jing-Hui Huang, Xiang-Yun Hu View a PDF of the paper titled Weak-Value Amplification for Longitudinal Phase Measurements Approaching the Shot-Noise Limit Characterized by Allan Variance, by Jing-Hui Huang and Xiang-Yun Hu View PDF HTML (experimental) Abstract:We report a quantitative evaluation of weak-value amplification (WVA) for longitudinal phase measurements using Allan variance analysis. Building on a recent double-slit interferometry experiment with real weak values [Phys. Rev. Lett. 134, 080802 (2025)], our Allan variance analysis demonstrates measurement of a few attosecond time delay approaching the shot noise limit at short averaging intervals of $T$ = $0.01-0.1$ s, representing two orders of magnitude variance reduction compared to the $T=300$ s operating point in prior implementations. We demonstrate that the Allan-variance noise floor scales with the inverse of the detected photon number $1/N_r$, confirming shot-noise-limited operation with WVA. Furthermore, this $1/N_r$ scaling experimentally validates that WVA can outperform conventional measurement under fixed detected photon number and detector saturation, in the presence of technical noise, as theoretically predicted [Phys. Rev. Lett. 118, 070802 (2017)]. Our results provide rigorous, quantitative evidence of the near-optimal noise performance achievable with WVA, establishing a new benchmark for precision optical metrology. This advancement is particularly relevant to applications such as gravitational-wave detection, where signals predominantly occupy the high-frequency regime ($>10$ Hz). Comments: Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2602.17035 [quant-ph] (or arXiv:2602.17035v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2602.17035 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Jing-Hui Huang [view email] [v1] Thu, 19 Feb 2026 03:06:52 UTC (6,949 KB) Full-text links: Access Paper: View a PDF of the paper titled Weak-Value Amplification for Longitudinal Phase Measurements Approaching the Shot-Noise Limit Characterized by Allan Variance, by Jing-Hui Huang and Xiang-Yun HuView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-02 References & Citations INSPIRE HEP NASA ADSGoogle Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv (What is alphaXiv?) Links to Code Toggle CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub Toggle DagsHub (What is DagsHub?) GotitPub Toggle Gotit.pub (What is GotitPub?) Huggingface Toggle Hugging Face (What is Huggingface?) Links to Code Toggle Papers with Code (What is Papers with Code?) ScienceCast Toggle ScienceCast (What is ScienceCast?) Demos Demos Replicate Toggle Replicate (What is Replicate?) Spaces Toggle Hugging Face Spaces (What is Spaces?) Spaces Toggle TXYZ.AI (What is TXYZ.AI?) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower (What are Influence Flowers?) Core recommender toggle CORE Recommender (What is CORE?) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs. Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)