{"id":505,"date":"2022-11-17T15:10:00","date_gmt":"2022-11-17T14:10:00","guid":{"rendered":"https:\/\/gqm.lpl.univ-paris13.fr\/?p=505"},"modified":"2025-10-28T14:42:47","modified_gmt":"2025-10-28T13:42:47","slug":"correlations-and-linewidth-of-the-atomic-beam-continuous-superradiant-laser","status":"publish","type":"post","link":"https:\/\/gqm.lpl.univ-paris13.fr\/index.php\/2022\/11\/17\/correlations-and-linewidth-of-the-atomic-beam-continuous-superradiant-laser\/","title":{"rendered":"Correlations and linewidth of the atomic beam continuous superradiant laser"},"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\">We focus on the case of weak single atom &#8211; cavity cooperativity, and highlight the relevant regime where decoherence due to the finite transit time dominates over spontaneous emission. <\/p>\n\n\n\n<p class=\"wp-block-paragraph\">We propose an original approach where the dynamics of atoms entering and leaving the cavity is described by a Hamiltonian process. This allows deriving the main dynamical equations for the superradiant laser, without the need for a stochastic approach. We derive analytical conditions for a sustained emission and show that the ultimate linewidth is set by the fundamental quantum fluctuations of the collective atomic dipole. <\/p>\n\n\n\n<p class=\"wp-block-paragraph\">We calculate steady-state values of the two-body correlators and show that the continuous superradiant regime is tied to the growth of atom-atom correlations, although these correlations only have a small impact on the laser linewidth.<\/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 is-resized has-custom-border is-style-rounded wp-duotone-unset-1\" id=\"wp-block-themeisle-blocks-image-483090ad\" 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\/10\/Correlation-and-linewidth-superradiant-529c9d.svg\" alt=\"\" class=\"wp-image-841\" style=\"border-style:none;border-width:0px;border-radius:10px;width:400px\"\/><figcaption class=\"wp-element-caption\">Steady-state correlator as a function of atom number. The correlator rapidly increases above the threshold for superradiance, but scales as 1\/N at large atom number.<\/figcaption><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>We propose a minimalistic model to account for the main properties of a continuous superradiant laser, in which a beam of atoms crosses the mode of a high-finesse Fabry-Perot cavity, and collectively emits light into the cavity mode.<br \/>\n<a href=\"https:\/\/doi.org\/10.48550\/arXiv.2210.05464\">arXiv:2210.05464 (2022)<\/a>  \/  <a href=\"https:\/\/doi.org\/10.21468\/SciPostPhysCore.6.1.015\">SciPost Phys. Core 6, 015 (2023)<\/a><\/p>\n","protected":false},"author":3,"featured_media":841,"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":[18,67],"tags":[28,26,36,93],"class_list":["post-505","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-article","category-superradiant","tag-benjamin-pasquiou","tag-bruno-laburthe-tolra","tag-martin-robert-de-saint-vincent","tag-ziyad-amodjee"],"blocksy_meta":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.6 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Correlations and linewidth of the atomic beam continuous superradiant laser - 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\/2022\/11\/17\/correlations-and-linewidth-of-the-atomic-beam-continuous-superradiant-laser\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Correlations and linewidth of the atomic beam continuous superradiant laser - Magnetic Quantum Gases\" \/>\n<meta property=\"og:description\" content=\"We propose a minimalistic model to account for the main properties of a continuous superradiant laser, in which a beam of atoms crosses the mode of a high-finesse Fabry-Perot cavity, and collectively emits light into the cavity mode. arXiv:2210.05464 (2022) \/ SciPost Phys. 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The correlator rapidly increases above the threshold for superradiance, but scales as 1\\\/N at large atom number.\"},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\\\/\\\/gqm.lpl.univ-paris13.fr\\\/index.php\\\/2022\\\/11\\\/17\\\/correlations-and-linewidth-of-the-atomic-beam-continuous-superradiant-laser\\\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\\\/\\\/gqm.lpl.univ-paris13.fr\\\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Correlations and linewidth of the atomic beam continuous superradiant laser\"}]},{\"@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 gases.\",\"publisher\":{\"@id\":\"https:\\\/\\\/gqm.lpl.univ-paris13.fr\\\/#organization\"},\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\\\/\\\/gqm.lpl.univ-paris13.fr\\\/?s={search_term_string}\"},\"query-input\":{\"@type\":\"PropertyValueSpecification\",\"valueRequired\":true,\"valueName\":\"search_term_string\"}}],\"inLanguage\":\"en-US\"},{\"@type\":\"Organization\",\"@id\":\"https:\\\/\\\/gqm.lpl.univ-paris13.fr\\\/#organization\",\"name\":\"Magnetic Quantum Gases\",\"url\":\"https:\\\/\\\/gqm.lpl.univ-paris13.fr\\\/\",\"logo\":{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\\\/\\\/gqm.lpl.univ-paris13.fr\\\/#\\\/schema\\\/logo\\\/image\\\/\",\"url\":\"https:\\\/\\\/gqm.lpl.univ-paris13.fr\\\/wp-content\\\/uploads\\\/2025\\\/10\\\/cropped-Condensation_512px.png\",\"contentUrl\":\"https:\\\/\\\/gqm.lpl.univ-paris13.fr\\\/wp-content\\\/uploads\\\/2025\\\/10\\\/cropped-Condensation_512px.png\",\"width\":512,\"height\":512,\"caption\":\"Magnetic Quantum Gases\"},\"image\":{\"@id\":\"https:\\\/\\\/gqm.lpl.univ-paris13.fr\\\/#\\\/schema\\\/logo\\\/image\\\/\"}},{\"@type\":\"Person\",\"@id\":\"https:\\\/\\\/gqm.lpl.univ-paris13.fr\\\/#\\\/schema\\\/person\\\/edd1441f419c30858a44ed007fc1fc79\",\"name\":\"Benjamin PASQUIOU\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\\\/\\\/secure.gravatar.com\\\/avatar\\\/f830cb90b39b89a47400329189c692407a76ff849fbc89ac7df353e712db23e0?s=96&d=mm&r=g\",\"url\":\"https:\\\/\\\/secure.gravatar.com\\\/avatar\\\/f830cb90b39b89a47400329189c692407a76ff849fbc89ac7df353e712db23e0?s=96&d=mm&r=g\",\"contentUrl\":\"https:\\\/\\\/secure.gravatar.com\\\/avatar\\\/f830cb90b39b89a47400329189c692407a76ff849fbc89ac7df353e712db23e0?s=96&d=mm&r=g\",\"caption\":\"Benjamin PASQUIOU\"},\"url\":\"https:\\\/\\\/gqm.lpl.univ-paris13.fr\\\/index.php\\\/author\\\/benjamin-pasquiou\\\/\"}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"Correlations and linewidth of the atomic beam continuous superradiant laser - Magnetic Quantum Gases","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/gqm.lpl.univ-paris13.fr\/index.php\/2022\/11\/17\/correlations-and-linewidth-of-the-atomic-beam-continuous-superradiant-laser\/","og_locale":"en_US","og_type":"article","og_title":"Correlations and linewidth of the atomic beam continuous superradiant laser - Magnetic Quantum Gases","og_description":"We propose a minimalistic model to account for the main properties of a continuous superradiant laser, in which a beam of atoms crosses the mode of a high-finesse Fabry-Perot cavity, and collectively emits light into the cavity mode. arXiv:2210.05464 (2022) \/ SciPost Phys. 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