Coherent Control of Coupled Nonlinear Microelectromechanical Resonators Under Parametric Modulation

Coherent Control of Coupled Nonlinear Microelectromechanical Resonators Under Parametric Modulation | 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 Coherent Control of Coupled Nonlinear Microelectromechanical Resonators Under Parametric Modulation Xiaolong Wen, Guijie Wang, Shenglin Hou, Najib Kacem, Lifang Ran, and 1 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6433281/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Coherent control of coupled microelectromechanical resonators within the framework of classical nonlinear dynamics is of relevance in fundamental studies and the development of high-performance sensors. Coherent control can be achieved through the parametric modulation of one of the two coupled resonators. However, microelectromechanical resonators are commonly operated in the nonlinear regime and a thorough description of key phenomena involving parametric modulation of coupled resonators, such as sideband generation and mode splitting, remains limited in this regime. Utilising a weakly coupled double-ended tuning fork (DETF) resonator under strong parametric modulation, we demonstrate tunable energy transfer and mode interactions governed by classical analogs of well-established quantum phenomena. This approach is theoretically assessed thanks to a nonlinear reduced order model which takes into account the modal interactions and virtual coupling induced by the parametric modulation. Furthermore, the proof of concept of the proposed tuning mechanism is validated on a DC electric field sensor with enhanced sensitivity. The nonlinear parametrically driven sensor exhibits a significant increment in sensitivity exceeding two orders of magnitude. while simultaneously maintaining a broad measurement range. While our findings remain within the classical regime, the observed dynamics and the simulation extend to the advancements of other cognate fields such as in optomechanics and two-level systems. Physical sciences/Engineering/Electrical and electronic engineering Physical sciences/Physics Full Text Additional Declarations There is no conflict of interest Supplementary Files SupplementaryInformation.pdf Cite Share Download PDF Status: Posted 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-6433281","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":442558977,"identity":"de220744-27c2-45fb-a561-42ab899d1726","order_by":0,"name":"Xiaolong Wen","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA+klEQVRIiWNgGAWjYDACZiB+AGEygugEIDYgrCUBygQqNSBCCwNCC5sEUVoMjjM/fJBQccduw/HeY9U8f/7kMbA3b5NgqLmDU4tkM5uxQcKZZ8kbzpxLu83bZlDMwHOsTILh2DOcWviZGcwkEtsOJ5vdyDG7zdtgkNggkWMmwdhwGKcWNmb2bxAt99+YFfP8AWqRf4NfCz8zD9gWO7MbPGbMPGwgW3jwa5Fs5ikG+uVwgv2ZHGPJuW3GxWw8acUWCcdwazE4f3zjgw8Vh+0l288YfnjzRy6Pn/3wxhsfanBrgYHEBrjvQEQCQQ0MDPZEqBkFo2AUjIKRCgBTdFIGt/BoowAAAABJRU5ErkJggg==","orcid":"https://orcid.org/0000-0001-7553-8778","institution":"Department of Physics, University of Science and Technology Beijing, Beijing Engineering Research Center of Detection and Application for Weak Magnetic Field","correspondingAuthor":true,"prefix":"","firstName":"Xiaolong","middleName":"","lastName":"Wen","suffix":""},{"id":442558978,"identity":"badb6e40-30dd-4d47-a3d2-b98c8c1a7840","order_by":1,"name":"Guijie Wang","email":"","orcid":"https://orcid.org/0009-0005-1660-994X","institution":"University of science and technology Beijing","correspondingAuthor":false,"prefix":"","firstName":"Guijie","middleName":"","lastName":"Wang","suffix":""},{"id":442558979,"identity":"3578abfa-1c7e-4011-b1ab-a46240cf8858","order_by":2,"name":"Shenglin Hou","email":"","orcid":"","institution":"University of Cambridge","correspondingAuthor":false,"prefix":"","firstName":"Shenglin","middleName":"","lastName":"Hou","suffix":""},{"id":442558980,"identity":"4f1e2610-aff4-4b74-94ce-da2f3cb53abe","order_by":3,"name":"Najib Kacem","email":"","orcid":"","institution":"Université Marie et Louis Pasteur","correspondingAuthor":false,"prefix":"","firstName":"Najib","middleName":"","lastName":"Kacem","suffix":""},{"id":442558981,"identity":"81489d78-00d7-4b69-9059-7539bdfff908","order_by":4,"name":"Lifang Ran","email":"","orcid":"","institution":"University of science and technology, Beijing","correspondingAuthor":false,"prefix":"","firstName":"Lifang","middleName":"","lastName":"Ran","suffix":""},{"id":442558982,"identity":"1109d5d5-833d-423f-a563-99b92e7249f6","order_by":5,"name":"Ashwin Seshia","email":"","orcid":"https://orcid.org/0000-0001-9305-6879","institution":"University of Cambridge","correspondingAuthor":false,"prefix":"","firstName":"Ashwin","middleName":"","lastName":"Seshia","suffix":""}],"badges":[],"createdAt":"2025-04-12 08:40:13","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-6433281/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6433281/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":80879332,"identity":"55ae51eb-995c-42b0-9e4a-c3e0190b9428","added_by":"auto","created_at":"2025-04-18 07:23:29","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1284657,"visible":true,"origin":"","legend":"","description":"","filename":"CoherentControlofCoupledNonlinearMicroelectromechanicalResonatorsUnderParametricModulation.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6433281/v1_covered_f191c320-4438-482e-b7ff-eae8c767b728.pdf"},{"id":80617145,"identity":"db70ca80-9b30-4b16-be26-bdfc106361fb","added_by":"auto","created_at":"2025-04-15 08:57:52","extension":"pdf","order_by":2,"title":"","display":"","copyAsset":false,"role":"supplement","size":3497401,"visible":true,"origin":"","legend":"","description":"","filename":"SupplementaryInformation.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6433281/v1/c0754f2b6529013a68f1cc93.pdf"}],"financialInterests":"There is no conflict of interest","formattedTitle":"Coherent Control of Coupled Nonlinear Microelectromechanical Resonators Under Parametric Modulation","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"","lastPublishedDoi":"10.21203/rs.3.rs-6433281/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6433281/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eCoherent control of coupled microelectromechanical resonators within the framework of classical nonlinear dynamics is of relevance in fundamental studies and the development of high-performance sensors. Coherent control can be achieved through the parametric modulation of one of the two coupled resonators. However, microelectromechanical resonators are commonly operated in the nonlinear regime and a thorough description of key phenomena involving parametric modulation of coupled resonators, such as sideband generation and mode splitting, remains limited in this regime. Utilising a weakly coupled double-ended tuning fork (DETF) resonator under strong parametric modulation, we demonstrate tunable energy transfer and mode interactions governed by classical analogs of well-established quantum phenomena. This approach is theoretically assessed thanks to a nonlinear reduced order model which takes into account the modal interactions and virtual coupling induced by the parametric modulation. Furthermore, the proof of concept of the proposed tuning mechanism is validated on a DC electric field sensor with enhanced sensitivity. The nonlinear parametrically driven sensor exhibits a significant increment in sensitivity exceeding two orders of magnitude. while simultaneously maintaining a broad measurement range. While our findings remain within the classical regime, the observed dynamics and the simulation extend to the advancements of other cognate fields such as in optomechanics and two-level systems.\u003c/p\u003e","manuscriptTitle":"Coherent Control of Coupled Nonlinear Microelectromechanical Resonators Under Parametric Modulation","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-04-15 08:57:47","doi":"10.21203/rs.3.rs-6433281/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"90473951-7548-448c-9701-6ac6218eb263","owner":[],"postedDate":"April 15th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":47112262,"name":"Physical sciences/Engineering/Electrical and electronic engineering"},{"id":47112263,"name":"Physical sciences/Physics"}],"tags":[],"updatedAt":"2025-04-18T07:15:20+00:00","versionOfRecord":[],"versionCreatedAt":"2025-04-15 08:57:47","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-6433281","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-6433281","identity":"rs-6433281","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}