Revealing inherent quantum interference and entanglement of a Dirac Fermion

preprint OA: closed CC-BY-4.0
📄 Open PDF Full text JSON View at publisher
AI-generated summary by claude@2026-07, 2026-07-15

This study reveals inherent quantum interference and entanglement of Dirac fermions, distinct from Zitterbewegung, by demonstrating phase-space quasiprobability negativity and pseudospin-momentum entanglement in simulations and experiments.

One-sentence paraphrase of the abstract; not a substitute for reading it. No clinical advice. How this works

AI-generated deep summary by claude@2026-07, 2026-07-15 · read from full text

The paper studies quantum dynamical Zitterbewegung for a Dirac fermion by asking whether it is underlain by a universal quantum interference phenomenon that lacks classical analogs. Using phase-space analysis, the authors identify an interference pattern whose nonclassical character is evidenced by negativity in a phase-space quasiprobability distribution, together with pseudospin–momentum entanglement, and they support the claim with numerical simulations and an on-chip experiment where a superconducting qubit and a quantized microwave field emulate internal and external Dirac degrees of freedom. A major caveat explicitly stated by the authors is that the work was presented as a preprint and had not yet undergone peer review at the time of posting. This paper does not explicitly discuss endometriosis or adenomyosis; it was included in the corpus via a keyword match in the upstream search index.

Read from the paper's body, not the abstract. Not a substitute for reading the paper. No clinical advice. How this works

Abstract

Abstract The Dirac equation is critical to understanding the universe, and plays an important role in technological advancements. Compared to the stationary solution, the dynamical evolution under the Dirac Hamiltonian is less understood, exemplified by Zitterbewegung. Although originally predicted in relativistic quantum mechanics, Zitterbewegung can also appear in some classical systems, which leads to the important question of whether Zitterbewegung of Dirac Fermions is underlain by a more fundamental and universal interference behavior without classical analogs. We here reveal such an interference pattern in phase space, which underlies but goes beyond Zitterbewegung, and whose nonclassicality is manifested by the negativity of the phase-space quasiprobability distribution, and the associated pseudospin-momentum entanglement. We confirm this discovery by numerical simulation and an on-chip experiment, where a superconducting qubit and a quantized microwave field respectively emulate the internal and external degrees of freedom of a Dirac particle. The measured quasiprobability negativities well agree with the numerical simulation. Besides being of fundamental importance, the demonstrated nonclassical effects are useful in quantum technology.
Full text 15,589 characters · extracted from preprint-html · click to expand
Revealing inherent quantum interference and entanglement of a Dirac Fermion | 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 Revealing inherent quantum interference and entanglement of a Dirac Fermion Wen Ning, Ri-Hua Zheng, Yan Xia, Kai Xu, Hekang Li, Dongning Zheng, and 4 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-2921505/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 10 Oct, 2023 Read the published version in npj Quantum Information → Version 1 posted 12 You are reading this latest preprint version Abstract The Dirac equation is critical to understanding the universe, and plays an important role in technological advancements. Compared to the stationary solution, the dynamical evolution under the Dirac Hamiltonian is less understood, exemplified by Zitterbewegung. Although originally predicted in relativistic quantum mechanics, Zitterbewegung can also appear in some classical systems, which leads to the important question of whether Zitterbewegung of Dirac Fermions is underlain by a more fundamental and universal interference behavior without classical analogs. We here reveal such an interference pattern in phase space, which underlies but goes beyond Zitterbewegung, and whose nonclassicality is manifested by the negativity of the phase-space quasiprobability distribution, and the associated pseudospin-momentum entanglement. We confirm this discovery by numerical simulation and an on-chip experiment, where a superconducting qubit and a quantized microwave field respectively emulate the internal and external degrees of freedom of a Dirac particle. The measured quasiprobability negativities well agree with the numerical simulation. Besides being of fundamental importance, the demonstrated nonclassical effects are useful in quantum technology. Physical sciences/Physics/Quantum physics/Quantum simulation Physical sciences/Physics/Quantum physics/Qubits Full Text Additional Declarations (Not answered) Supplementary Files SI.pdf Cite Share Download PDF Status: Published Journal Publication published 10 Oct, 2023 Read the published version in npj Quantum Information → Version 1 posted Editorial decision: revise 18 Jul, 2023 Review # 3 received at journal 13 Jul, 2023 Review # 2 received at journal 30 Jun, 2023 Reviewer # 3 agreed at journal 11 Jun, 2023 Reviewer # 2 agreed at journal 07 Jun, 2023 Review # 1 received at journal 28 May, 2023 Reviewer # 1 agreed at journal 15 May, 2023 Reviewers invited by journal 14 May, 2023 Submission checks completed at journal 09 May, 2023 First submitted to journal 05 May, 2023 Unknown event 05 May, 2023 Editor assigned by journal 04 May, 2023 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-2921505","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":200373866,"identity":"7230a904-e899-4874-b6db-182c9f8af0a0","order_by":0,"name":"Wen Ning","email":"","orcid":"","institution":"Fuzhou University","correspondingAuthor":false,"prefix":"","firstName":"Wen","middleName":"","lastName":"Ning","suffix":""},{"id":200373867,"identity":"53f6fcb8-9fef-4944-98b1-d7841ba9af6d","order_by":1,"name":"Ri-Hua Zheng","email":"","orcid":"","institution":"Fuzhou University","correspondingAuthor":false,"prefix":"","firstName":"Ri-Hua","middleName":"","lastName":"Zheng","suffix":""},{"id":200373868,"identity":"488195a9-fd45-42ea-b084-0725f3fb1548","order_by":2,"name":"Yan Xia","email":"","orcid":"","institution":"Fuzhou University","correspondingAuthor":false,"prefix":"","firstName":"Yan","middleName":"","lastName":"Xia","suffix":""},{"id":200373869,"identity":"4d93b027-dee2-4d9f-95d6-54fc28f164a7","order_by":3,"name":"Kai Xu","email":"","orcid":"https://orcid.org/0000-0002-7776-2455","institution":"Institute of Physics, Chinese Academy of Sciences","correspondingAuthor":false,"prefix":"","firstName":"Kai","middleName":"","lastName":"Xu","suffix":""},{"id":200373870,"identity":"8636e21c-b053-49ff-9111-793645d97e85","order_by":4,"name":"Hekang Li","email":"","orcid":"https://orcid.org/0000-0003-3914-4979","institution":"Institute of Physics, Chinese Academy of Sciences","correspondingAuthor":false,"prefix":"","firstName":"Hekang","middleName":"","lastName":"Li","suffix":""},{"id":200373871,"identity":"0e74c2fb-b6b5-4b7c-be46-3fd3f363bc10","order_by":5,"name":"Dongning Zheng","email":"","orcid":"https://orcid.org/0000-0001-5895-0111","institution":"Chinese Academy of Sciences","correspondingAuthor":false,"prefix":"","firstName":"Dongning","middleName":"","lastName":"Zheng","suffix":""},{"id":200373872,"identity":"387aa1c6-0d19-4b6e-94d7-ef1bf3dca3f2","order_by":6,"name":"Heng Fan","email":"","orcid":"https://orcid.org/0000-0002-5328-2449","institution":"Institute of Physics, Chinese Academy of Sciences","correspondingAuthor":false,"prefix":"","firstName":"Heng","middleName":"","lastName":"Fan","suffix":""},{"id":200373873,"identity":"434d4b15-a68b-4aaa-9508-296cc2cca56e","order_by":7,"name":"Zhen-Biao Yang","email":"","orcid":"https://orcid.org/0000-0002-3964-4714","institution":"Fuzhou University","correspondingAuthor":false,"prefix":"","firstName":"Zhen-Biao","middleName":"","lastName":"Yang","suffix":""},{"id":200373874,"identity":"f68b9276-909d-4b55-bea0-9176d4fcf052","order_by":8,"name":"Shi-Biao Zheng","email":"","orcid":"","institution":"Fuzhou University","correspondingAuthor":false,"prefix":"","firstName":"Shi-Biao","middleName":"","lastName":"Zheng","suffix":""},{"id":200373875,"identity":"bc466d15-bfbf-4083-8131-12d1f3df9d8d","order_by":9,"name":"Fan Wu","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAzElEQVRIiWNgGAWjYDAC9saGAx8MbPjBHB5idPDwHG58OKMiTbKBeC0S6c3GHGcOk6DFniGxTZqx7byE/IwExgdv2xjkzQnawnCwTbqw7bYE44wEZsO5bQyGOxsIaWFsbJOe2Xa7jlkigU2at40hweAAIS3MjG1Aleck2CQS2H8Tp4WNsdmY58wBCR6gLczEaTnDCArkZAkJnofNknPOSRhuIKSFff7zB8CotJOQb08++OFNmY08QVuQAGMDkJAgXv0oGAWjYBSMAtwAAGLRPGBOfBgpAAAAAElFTkSuQmCC","orcid":"","institution":"Fuzhou University","correspondingAuthor":true,"prefix":"","firstName":"Fan","middleName":"","lastName":"Wu","suffix":""}],"badges":[],"createdAt":"2023-05-11 19:21:02","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-2921505/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-2921505/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1038/s41534-023-00770-0","type":"published","date":"2023-10-10T04:00:00+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":44412801,"identity":"b8671f7d-6982-4660-8318-7cedd2e29f47","added_by":"auto","created_at":"2023-10-11 07:11:15","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1819930,"visible":true,"origin":"","legend":"","description":"","filename":"Dirac.pdf","url":"https://assets-eu.researchsquare.com/files/rs-2921505/v1_covered_36767e8d-90d9-43db-a3fe-5b2c4e8a5ba1.pdf"},{"id":37117743,"identity":"6eeed79f-50de-48c6-b806-d1aad4b2c3e5","added_by":"auto","created_at":"2023-05-17 03:15:12","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":3537331,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cbr\u003e\u003c/p\u003e","description":"","filename":"SI.pdf","url":"https://assets-eu.researchsquare.com/files/rs-2921505/v1/deb2fb0f8d49fc05e2d84a51.pdf"}],"financialInterests":"(Not answered)","formattedTitle":"Revealing inherent quantum interference and entanglement of a Dirac Fermion","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"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":"npj-quantum-information","isNatureJournal":false,"hasQc":false,"allowDirectSubmit":false,"externalIdentity":"npjqi","sideBox":"Learn more about [npj Quantum Information](http://www.nature.com/npjqi/)","snPcode":"41534","submissionUrl":"https://mts-npjqi.nature.com/","title":"npj Quantum Information","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"ejp","reportingPortfolio":"NPJ","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"","lastPublishedDoi":"10.21203/rs.3.rs-2921505/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-2921505/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"The Dirac equation is critical to understanding the universe, and plays an important role in technological advancements. Compared to the stationary solution, the dynamical evolution under the Dirac Hamiltonian is less understood, exemplified by Zitterbewegung. Although originally predicted in relativistic quantum mechanics, Zitterbewegung can also appear in some classical systems, which leads to the important question of whether Zitterbewegung of Dirac Fermions is underlain by a more fundamental and universal interference behavior without classical analogs. We here reveal such an interference pattern in phase space, which underlies but goes beyond Zitterbewegung, and whose nonclassicality is manifested by the negativity of the phase-space quasiprobability distribution, and the associated pseudospin-momentum entanglement. We confirm this discovery by numerical simulation and an on-chip experiment, where a superconducting qubit and a quantized microwave field respectively emulate the internal and external degrees of freedom of a Dirac particle. The measured quasiprobability negativities well agree with the numerical simulation. Besides being of fundamental importance, the demonstrated nonclassical effects are useful in quantum technology.","manuscriptTitle":"Revealing inherent quantum interference and entanglement of a Dirac Fermion","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2023-05-17 03:15:07","doi":"10.21203/rs.3.rs-2921505/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"revise","date":"2023-07-18T05:03:33+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"This content is not available.","date":"2023-07-13T20:36:40+00:00","index":3,"fulltext":"This content is not available."},{"type":"editorInvitedReview","content":"This content is not available.","date":"2023-06-30T21:52:06+00:00","index":2,"fulltext":"This content is not available."},{"type":"reviewerAgreed","content":"This content is not available.","date":"2023-06-11T12:11:24+00:00","index":3,"fulltext":"This content is not available."},{"type":"reviewerAgreed","content":"This content is not available.","date":"2023-06-07T11:40:41+00:00","index":2,"fulltext":"This content is not available."},{"type":"editorInvitedReview","content":"This content is not available.","date":"2023-05-29T00:00:22+00:00","index":1,"fulltext":"This content is not available."},{"type":"reviewerAgreed","content":"This content is not available.","date":"2023-05-15T10:53:44+00:00","index":1,"fulltext":"This content is not available."},{"type":"reviewersInvited","content":"","date":"2023-05-15T01:35:04+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2023-05-09T10:09:07+00:00","index":"","fulltext":""},{"type":"submitted","content":"npj Quantum Information","date":"2023-05-06T03:24:07+00:00","index":"","fulltext":""},{"type":"checksFailed","content":"","date":"2023-05-05T14:51:57+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2023-05-04T14:58:42+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"npj-quantum-information","isNatureJournal":false,"hasQc":false,"allowDirectSubmit":false,"externalIdentity":"npjqi","sideBox":"Learn more about [npj Quantum Information](http://www.nature.com/npjqi/)","snPcode":"41534","submissionUrl":"https://mts-npjqi.nature.com/","title":"npj Quantum Information","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"ejp","reportingPortfolio":"NPJ","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"18d3798b-535d-4bb3-b0c3-0600e6ce65cd","owner":[],"postedDate":"May 17th, 2023","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[{"id":21500630,"name":"Physical sciences/Physics/Quantum physics/Quantum simulation"},{"id":21500631,"name":"Physical sciences/Physics/Quantum physics/Qubits"}],"tags":[],"updatedAt":"2023-10-11T07:11:01+00:00","versionOfRecord":{"articleIdentity":"rs-2921505","link":"https://doi.org/10.1038/s41534-023-00770-0","journal":{"identity":"npj-quantum-information","isVorOnly":false,"title":"npj Quantum Information"},"publishedOn":"2023-10-10 04:00:00","publishedOnDateReadable":"October 10th, 2023"},"versionCreatedAt":"2023-05-17 03:15:07","video":"","vorDoi":"10.1038/s41534-023-00770-0","vorDoiUrl":"https://doi.org/10.1038/s41534-023-00770-0","workflowStages":[]},"version":"v1","identity":"rs-2921505","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-2921505","identity":"rs-2921505","version":["v1"]},"buildId":"_2-kVJe1T_tPrBINL-cwx","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}

Text is read by the "Ask this paper" AI Q&A widget below. Extraction quality varies by source — PMC NXML preserves structure cleanly, OA-HTML may include some navigation residue, and OA-PDF can have broken hyphenation. The publisher copy (via DOI) is the canonical version.

My notes (saved in your browser only)

Ask this paper AI returns verbatim quotes from the full text · source: preprint-html

Answers must be backed by verbatim quotes from this paper's full text. Hallucinated quotes are dropped automatically; if no verbatim passage answers the question, we say so. How this works

Citation neighborhood (no data yet)

We don't have any in-corpus citations linked to this paper yet. The paper's references may be in our DB but unresolved to ``paper_id`` (resolution happens at ingest when the cited DOI matches a row we already have). Run the cross-source citation reconcile pass to retry.

Source provenance

europepmc
last seen: 2026-05-19T01:45:01.086888+00:00
unpaywall
last seen: 2026-05-22T02:00:06.705733+00:00
License: CC-BY-4.0