{"id":496,"date":"2024-10-07T14:47:00","date_gmt":"2024-10-07T12:47:00","guid":{"rendered":"https:\/\/gqm.lpl.univ-paris13.fr\/?p=496"},"modified":"2025-11-08T15:16:52","modified_gmt":"2025-11-08T14:16:52","slug":"effective-light-induced-hamiltonian-for-atoms-with-large-nuclear-spin","status":"publish","type":"post","link":"https:\/\/gqm.lpl.univ-paris13.fr\/index.php\/2024\/10\/07\/effective-light-induced-hamiltonian-for-atoms-with-large-nuclear-spin\/","title":{"rendered":"Effective light-induced Hamiltonian for atoms with large nuclear spin"},"content":{"rendered":"\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-995f960e wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:66.66%\">\n<p class=\"wp-block-paragraph\">Ultracold fermionic atoms, having two valence electrons, exhibit a distinctive internal state structure, wherein the nuclear spin becomes decoupled from the electronic degrees of freedom in the ground electronic state. Consequently, the nuclear spin states are well isolated from the environment, rendering these atomic systems an opportune platform for quantum computation and quantum simulations. Coupling with off-resonance light is an essential tool to selectively and coherently manipulate the nuclear spin states.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">In this paper, we present a systematic derivation of the effective Hamiltonian for the nuclear spin states of ultracold fermionic atoms due to such an off-resonance light. We obtain compact expressions for the scalar, vector, and tensor light shifts taking into account both linear and quadratic contributions to the hyperfine splitting. The analysis has been carried out using the Green operator approach and solving the corresponding Dyson equation.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Finally, we analyze different scenarios of light configurations which lead to the vector- and tensor-light shifts, as well as the pure spin-orbit coupling for the nuclear spin.<\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:33.33%\">\n<figure class=\"wp-block-image aligncenter size-full has-custom-border is-style-rounded wp-duotone-unset-1\" id=\"wp-block-themeisle-blocks-image-00e18308\" style=\"margin-top:var(--wp--preset--spacing--20);margin-right:var(--wp--preset--spacing--20);margin-bottom:var(--wp--preset--spacing--20);margin-left:var(--wp--preset--spacing--20)\"><img loading=\"lazy\" decoding=\"async\" width=\"300\" height=\"300\" src=\"https:\/\/gqm.lpl.univ-paris13.fr\/wp-content\/uploads\/2025\/11\/Article-Effective-light-induced-Hamiltonian-8702da.svg\" alt=\"\" class=\"wp-image-1633\" style=\"border-style:none;border-width:0px;border-radius:10px\"\/><figcaption class=\"wp-element-caption\">Dependence of the rescaled scalar b0 (a), vector b1 and tensor b2 coefficients (b) on the rescaled detuning \u2206 for iI = 9\/2 and \u03b3 = 0.006, corresponding to 87Sr atoms.<\/figcaption><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>In this paper, we present a systematic derivation of the effective Hamiltonian for the nuclear spin states of ultracold fermionic atoms due to such an off-resonance light. We obtain compact expressions for the scalar, vector, and tensor light shifts taking into account both linear and quadratic contributions to the hyperfine splitting.<br \/>\n<a href=\"https:\/\/doi.org\/10.48550\/arXiv.2404.12429\">arXiv:2404.12429 (2024)<\/a>  \/  <a href=\"https:\/\/doi.org\/10.1103\/PhysRevResearch.6.033293\">Phys. Rev. Research 6, 033293 (2024)<\/a><\/p>\n","protected":false},"author":3,"featured_media":1633,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_themeisle_gutenberg_block_has_review":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[18,65],"tags":[81,84,87,82,36],"class_list":["post-496","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-article","category-strontium","tag-domantas-burba","tag-emilia-witkowska","tag-gediminas-juzeliunas","tag-hubert-dunikowski","tag-martin-robert-de-saint-vincent"],"blocksy_meta":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.6 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Effective light-induced Hamiltonian for atoms with large nuclear spin - Magnetic Quantum Gases<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/gqm.lpl.univ-paris13.fr\/index.php\/2024\/10\/07\/effective-light-induced-hamiltonian-for-atoms-with-large-nuclear-spin\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Effective light-induced Hamiltonian for atoms with large nuclear spin - Magnetic Quantum Gases\" \/>\n<meta property=\"og:description\" content=\"In this paper, we present a systematic derivation of the effective Hamiltonian for the nuclear spin states of ultracold fermionic atoms due to such an off-resonance light. We obtain compact expressions for the scalar, vector, and tensor light shifts taking into account both linear and quadratic contributions to the hyperfine splitting. arXiv:2404.12429 (2024) \/ Phys. Rev. Research 6, 033293 (2024)\" \/>\n<meta property=\"og:url\" content=\"https:\/\/gqm.lpl.univ-paris13.fr\/index.php\/2024\/10\/07\/effective-light-induced-hamiltonian-for-atoms-with-large-nuclear-spin\/\" \/>\n<meta property=\"og:site_name\" content=\"Magnetic Quantum Gases\" \/>\n<meta property=\"article:published_time\" content=\"2024-10-07T12:47:00+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2025-11-08T14:16:52+00:00\" \/>\n<meta name=\"author\" content=\"Benjamin PASQUIOU\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"Benjamin PASQUIOU\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"1 minute\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\\\/\\\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\\\/\\\/gqm.lpl.univ-paris13.fr\\\/index.php\\\/2024\\\/10\\\/07\\\/effective-light-induced-hamiltonian-for-atoms-with-large-nuclear-spin\\\/#article\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/gqm.lpl.univ-paris13.fr\\\/index.php\\\/2024\\\/10\\\/07\\\/effective-light-induced-hamiltonian-for-atoms-with-large-nuclear-spin\\\/\"},\"author\":{\"name\":\"Benjamin PASQUIOU\",\"@id\":\"https:\\\/\\\/gqm.lpl.univ-paris13.fr\\\/#\\\/schema\\\/person\\\/edd1441f419c30858a44ed007fc1fc79\"},\"headline\":\"Effective light-induced Hamiltonian for atoms with large nuclear spin\",\"datePublished\":\"2024-10-07T12:47:00+00:00\",\"dateModified\":\"2025-11-08T14:16:52+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\\\/\\\/gqm.lpl.univ-paris13.fr\\\/index.php\\\/2024\\\/10\\\/07\\\/effective-light-induced-hamiltonian-for-atoms-with-large-nuclear-spin\\\/\"},\"wordCount\":200,\"publisher\":{\"@id\":\"https:\\\/\\\/gqm.lpl.univ-paris13.fr\\\/#organization\"},\"image\":{\"@id\":\"https:\\\/\\\/gqm.lpl.univ-paris13.fr\\\/index.php\\\/2024\\\/10\\\/07\\\/effective-light-induced-hamiltonian-for-atoms-with-large-nuclear-spin\\\/#primaryimage\"},\"thumbnailUrl\":\"https:\\\/\\\/gqm.lpl.univ-paris13.fr\\\/wp-content\\\/uploads\\\/2025\\\/11\\\/Article-Effective-light-induced-Hamiltonian-8702da.svg\",\"keywords\":[\"Domantas Burba\",\"Emilia Witkowska\",\"Gediminas Juzeli\u016bnas\",\"Hubert Dunikowski\",\"Martin Robert-de-Saint-Vincent\"],\"articleSection\":[\"Article\",\"Strontium\"],\"inLanguage\":\"en-US\"},{\"@type\":\"WebPage\",\"@id\":\"https:\\\/\\\/gqm.lpl.univ-paris13.fr\\\/index.php\\\/2024\\\/10\\\/07\\\/effective-light-induced-hamiltonian-for-atoms-with-large-nuclear-spin\\\/\",\"url\":\"https:\\\/\\\/gqm.lpl.univ-paris13.fr\\\/index.php\\\/2024\\\/10\\\/07\\\/effective-light-induced-hamiltonian-for-atoms-with-large-nuclear-spin\\\/\",\"name\":\"Effective light-induced Hamiltonian for atoms with large nuclear spin - 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of the rescaled scalar b0 (a), vector b1 and tensor b2 coefficients (b) on the rescaled detuning \u2206 for iI = 9\/2 and \u03b3 = 0.006, corresponding to 87Sr atoms."},{"@type":"BreadcrumbList","@id":"https:\/\/gqm.lpl.univ-paris13.fr\/index.php\/2024\/10\/07\/effective-light-induced-hamiltonian-for-atoms-with-large-nuclear-spin\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/gqm.lpl.univ-paris13.fr\/"},{"@type":"ListItem","position":2,"name":"Effective light-induced Hamiltonian for atoms with large nuclear spin"}]},{"@type":"WebSite","@id":"https:\/\/gqm.lpl.univ-paris13.fr\/#website","url":"https:\/\/gqm.lpl.univ-paris13.fr\/","name":"Magnetic Quantum Gases","description":"Explore quantum magnetism with ultra-cold atom 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