Probing minimal observable length with dark modes in an optomechanical detector

Probing minimal observable length with dark modes in an optomechanical detector | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article Probing minimal observable length with dark modes in an optomechanical detector Wenlin Li, Xingli Li, Najmeh Eshaqi-Sani, Wen-zhao Zhang, Jiong Cheng This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7422859/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted You are reading this latest preprint version Abstract Several theories that attempt to unify quantum theory and gravitational theory assume that space has an observable limiting resolution related to the Planck length, denoted by √ β0Lp. Quantum mechanically, this concept derives a generalized uncertainty principle (GUP) and the corresponding modified commutator. The prediction and observation of GUP-induced new physics, as well as the quantitative measurement of the value of β0, may provide substantial support for the establishment of quantum gravity theory. In this paper, we propose a comprehensive quantum framework for measuring GUP at low energy scales by utilizing the interference-induced bright-dark mode effect of oscillators in an optomechanical system. The nonlinearity induced by GUP will be amplified by the bright mode dynamics, and then be quantitatively read out by the noise spectrum of the dark mode. The measurement limit resolution of the scheme is not constrained by the quality factor of the oscillator. Under experimentally achievable parameters, the measurement resolution has been shown to reach βNL,lim = 10−16.75, which is 10 orders of magnitude lower than the electroweak level. Physical sciences/Optics and photonics/Optical physics/Quantum optics Physical sciences/Physics/Quantum physics/Quantum metrology Full Text Additional Declarations There is NO Competing Interest. Cite Share Download PDF Status: Under Review Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-7422859","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":503599098,"identity":"46a3517b-d952-445b-938f-386035bb5dd0","order_by":0,"name":"Wenlin Li","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA80lEQVRIiWNgGAWjYBACPmYQWSDBwA+kDjyAikrg08IG1mIgwSDZANSSQJQWMGkARAeANHFa2HkMHxcYWOQZXzv8EGjLHTmDA8wHb/Mw2OXhdhiPsfEMA4lis9tpBkAtz4wNDrAlW/MwJBfj1sK7TZrHQCJx2+0EkJbDiRsO8JhJ8zAcSGzArWX7b5CWzbPTP4C01G84wP+NkJZtzCAtG6RzwLYA7eJhI6CF/zPYYTNu5xQcSDA4bDjzMJux5RyDZJxa+PmPJX7mqahL7J+dvvnDh4rD8nzHmx/eeFNhh1MLGgBGEAMzjDEKRsEoGAWjgGwAAPabT1boVJ46AAAAAElFTkSuQmCC","orcid":"https://orcid.org/0000-0003-2032-0530","institution":"College of Sciences, Northeastern University","correspondingAuthor":true,"prefix":"","firstName":"Wenlin","middleName":"","lastName":"Li","suffix":""},{"id":503599099,"identity":"503104b9-3ec7-4f84-b239-1c2e4d84f717","order_by":1,"name":"Xingli Li","email":"","orcid":"","institution":"Department of Physics, The Chinese University of Hong Kong","correspondingAuthor":false,"prefix":"","firstName":"Xingli","middleName":"","lastName":"Li","suffix":""},{"id":503599100,"identity":"d52ba2ec-526e-4932-b2c0-6b78e2349d95","order_by":2,"name":"Najmeh Eshaqi-Sani","email":"","orcid":"","institution":"Department of Mathematical, Physical and Computer Sciences, University of Parma","correspondingAuthor":false,"prefix":"","firstName":"Najmeh","middleName":"","lastName":"Eshaqi-Sani","suffix":""},{"id":503599101,"identity":"5847f24d-4b50-4a3b-9681-6c2d6510f36d","order_by":3,"name":"Wen-zhao Zhang","email":"","orcid":"","institution":"Ningbo University","correspondingAuthor":false,"prefix":"","firstName":"Wen-zhao","middleName":"","lastName":"Zhang","suffix":""},{"id":503599102,"identity":"e6485ecc-dda6-4ac5-9d2d-d38ec4be83fb","order_by":4,"name":"Jiong Cheng","email":"","orcid":"","institution":"Ningbo University","correspondingAuthor":false,"prefix":"","firstName":"Jiong","middleName":"","lastName":"Cheng","suffix":""}],"badges":[],"createdAt":"2025-08-21 06:25:16","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-7422859/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7422859/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":90358045,"identity":"4f283222-05b6-4050-9e7b-7e76bdab2048","added_by":"auto","created_at":"2025-09-01 22:43:25","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1090629,"visible":true,"origin":"","legend":"Article File","description":"","filename":"darkGUPV1.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7422859/v1_covered_6e20cc8c-f823-476b-905d-a7abbea7f7c1.pdf"}],"financialInterests":"There is \u003cb\u003eNO\u003c/b\u003e Competing Interest.","formattedTitle":"Probing minimal observable length with dark modes in an optomechanical detector","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"nature-portfolio","isNatureJournal":true,"hasQc":false,"allowDirectSubmit":false,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"","title":"Nature Portfolio","twitterHandle":"","acdcEnabled":false,"dfaEnabled":false,"editorialSystem":"ejp","reportingPortfolio":"","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"","lastPublishedDoi":"10.21203/rs.3.rs-7422859/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7422859/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eSeveral theories that attempt to unify quantum theory and gravitational theory assume that space has an observable limiting resolution related to the Planck length, denoted by √ β0Lp. Quantum mechanically, this concept derives a generalized uncertainty principle (GUP) and the corresponding modified commutator. The prediction and observation of GUP-induced new physics, as well as the quantitative measurement of the value of β0, may provide substantial support for the establishment of quantum gravity theory. In this paper, we propose a comprehensive quantum framework for measuring GUP at low energy scales by utilizing the interference-induced bright-dark mode effect of oscillators in an optomechanical system. The nonlinearity induced by GUP will be amplified by the bright mode dynamics, and then be quantitatively read out by the noise spectrum of the dark mode. The measurement limit resolution of the scheme is not constrained by the quality factor of the oscillator. 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