{"id":597,"date":"2019-11-08T14:32:00","date_gmt":"2019-11-08T13:32:00","guid":{"rendered":"https:\/\/gqm.lpl.univ-paris13.fr\/?p=597"},"modified":"2025-10-28T15:23:38","modified_gmt":"2025-10-28T14:23:38","slug":"theoretical-analysis-of-the-excitations-and-instabilities-of-spinor-dipolar-bose-einstein-condensates","status":"publish","type":"post","link":"https:\/\/gqm.lpl.univ-paris13.fr\/index.php\/2019\/11\/08\/theoretical-analysis-of-the-excitations-and-instabilities-of-spinor-dipolar-bose-einstein-condensates\/","title":{"rendered":"Theoretical analysis of the excitations and instabilities of spinor dipolar Bose-Einstein condensates"},"content":{"rendered":"\n
<\/div>
\n
\n

Abstract:<\/strong><\/h4>\n\n\n\n

In spinor Bose-Einstein condensates (SBEC), several spin states coexist, giving rise to dynamics driven by spin-dependent interactions (contact (CI) and dipole-dipole (DDI) interactions). In close connection with the experimental work of our group, this thesis presents a theoretical analysis of the dynamical behavior of SBEC which are initially in the ferromagnetic fully polarized ground state, and set out of equilibrium. <\/p>\n\n\n\n

Within the Bogolyubov theory, we analyzed the excitations of a uniform spin f<\/em> condensate. Our study highlights the existence of dynamical instabilities when the applied magnetic field is less than critical field pdd<\/sub> which is of the order of \u223c0.1mG. It is shown that pdd<\/sub> is only set by the DDI. The growth of dynamical instability gives rise to spin texture formation and demagnetization dynamics. For trapped condensates, our Gross-Pitaevskii simulations show demagnetization dynamics below the critical field pdem<\/sub>\u2272pdd<\/sub>.<\/p>\n\n\n\n

We also studied the dynamics of trapped condensate in the presence of a strong magnetic field \u223c200mG\u226bpdd<\/sub>, and a gradient \u223c10mG\/cm. The initial state is excited by performing an overall rotation of the spins. We have highlighted two new phenomena. First, our Gross-Pitaevskii simulations show an unexpected preservation of the initial ferromagnetic character (the DDI and the gradient can modify this ferromagnetic character). By neglecting the DDI, we show that this preservation is the result of a competition between two effects : the kinetic energy acquired by the spin components in the presence of the gradient tends to modify the ferromagnetic character. This effect is inhibited by the CI which imposes an energy gap. Secondly, for trapped condensates, spin collective behavior is demonstrated: the spins oscillate around their initial orientation with an amplitude that varies spatially and a frequency of the order of \u210f\/M\u03c32<\/sup>\u226a\u03c9 (\u03c3 is the size of the condensate and \u03c9\/2\u03c0 is the frequency of the trap). Our calculations are in excellent agreement with experimental results.<\/p>\n\n\n\n

\n
\n
2019 – Thesis – Kaci Kechadi<\/a>Download<\/a><\/div>\n<\/div>\n\n\n\n
\n

Link to HAL<\/a><\/p>\n<\/div>\n<\/div>\n<\/div>\n\n\n\n

\n

Soutenance de th\u00e8se de Kaci Kechadi<\/em>
Date:<\/strong> Vendredi 8 novembre 2019
Location:<\/strong> Laboratoire de Physique des Lasers, 99 av. J.B. Cl\u00e9ment 93430 Villetaneuse France<\/p>\n\n\n\n

Keywords:<\/strong><\/h4>\n\n\n\n

Spinor Bose-Einstein condensation, dipolar interaction, Bogolyubov theory, collective spin modes, Gross-Pitaevskii simulations.<\/p>\n\n\n\n

Jury:<\/strong><\/h4>\n\n\n\n
    \n
  • Nicolas Pavloff (President)<\/li>\n\n\n\n
  • Anna Minguzzi (Referee)<\/li>\n\n\n\n
  • Patrizia Vignolo (Referee)<\/li>\n\n\n\n
  • Paolo Pedri (Co-supervisor)<\/li>\n\n\n\n
  • Bruno Laburthe-Tolra (Supervisor)<\/li>\n<\/ul>\n<\/div>\n<\/div><\/div>\n\n\n\n

    French version:<\/h4>\n\n\n\n

    Analyse th\u00e9orique des excitations et des instabilit\u00e9s des condensats de Bose-Einstein spinoriels dipolaires<\/h3>\n\n\n\n

    Dans les condensats de Bose-Einstein spinoriels (CBES), plusieurs \u00e9tats de spin coexistent, donnant lieu \u00e0 des dynamiques pilot\u00e9es par des interactions d\u00e9pendantes du spin (interactions de contact (IC) et dip\u00f4le-dip\u00f4le (IDD)). En lien \u00e9troit avec les travaux exp\u00e9rimentaux de notre groupe, ce manuscrit pr\u00e9sente une analyse th\u00e9orique du comportement dynamique des CBES. On s\u2019int\u00e9resse \u00e0 la situation o\u00f9 les CBES se trouvent dans l\u2019\u00e9tat fondamental ferromagn\u00e9tique \u00e0 magn\u00e9tisation maximale, et qui sont port\u00e9s hors de l\u2019\u00e9tat d\u2019\u00e9quilibre. En analysant les instabilit\u00e9s d\u2019un condensat uniforme de spin f<\/em> dans le cadre de la th\u00e9orie de Bogoliubov, on met en \u00e9vidence l\u2019existence d\u2019instabilit\u00e9s dynamiques lorsque le champ magn\u00e9tique appliqu\u00e9 est inf\u00e9rieur \u00e0 un champ critique pdd<\/sub> qui est de l\u2019ordre de \u223c0.1mG. On montre que pdd<\/sub> est fix\u00e9 uniquement par l\u2019IDD. L\u2019instabilit\u00e9 se traduit par l\u2019apparition de textures de spin et par la d\u00e9magn\u00e9tisation du condensat. Pour un condensat pi\u00e9g\u00e9, nos simulations num\u00e9riques bas\u00e9es sur l\u2019\u00e9quation de Gross-Pitaevskii montrent une d\u00e9magn\u00e9tisation pour un champ critique pdem<\/sub>\u2272pdd<\/sub>.<\/p>\n\n\n\n

    Nous avons \u00e9galement \u00e9tudi\u00e9 les dynamiques du condensat pi\u00e9g\u00e9 en pr\u00e9sence d\u2019un fort champ magn\u00e9tique \u223c200mG\u226bpdd<\/sub>, et d\u2019un gradient \u223c10mG\/cm. L\u2019\u00e9tat initial est excit\u00e9 en effectuant une rotation globale des spins. Nos simulations num\u00e9riques (Gross-Pitaevskii) montrent une persistance inattendue du caract\u00e8re ferromagn\u00e9tique initial. On montre que l\u2019\u00e9nergie cin\u00e9tique communiqu\u00e9e par le gradient aux \u00e9tats de spin tend \u00e0 alt\u00e9rer le caract\u00e8re ferromagn\u00e9tique, mais que cet effet est contrebalanc\u00e9 par l\u2019IC qui impose un gap en \u00e9nergie. Enfin, pour un condensat pi\u00e9g\u00e9, on met en \u00e9vidence des modes collectifs de spin : les spins oscillent autour de leur orientation initiale avec une amplitude qui varie spatialement et une fr\u00e9quence de l\u2019ordre de \u210f\/M\u03c32<\/sup>\u226a\u03c9 (\u03c3 est la taille du condensat et \u03c9\/2\u03c0 la fr\u00e9quence du pi\u00e8ge). La comparaison de nos calculs avec les exp\u00e9riences montre un excellent accord.<\/p>\n","protected":false},"excerpt":{"rendered":"

    French version: Analyse th\u00e9orique des excitations et des instabilit\u00e9s des condensats de Bose-Einstein spinoriels dipolaires Dans les condensats de Bose-Einstein spinoriels (CBES), plusieurs \u00e9tats de spin coexistent, donnant lieu \u00e0 des dynamiques pilot\u00e9es par des interactions d\u00e9pendantes du spin (interactions de contact (IC) et dip\u00f4le-dip\u00f4le (IDD)). En lien \u00e9troit avec les travaux exp\u00e9rimentaux de notre […]<\/p>\n","protected":false},"author":3,"featured_media":0,"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":[75],"tags":[155],"class_list":["post-597","post","type-post","status-publish","format-standard","hentry","category-phd-thesis","tag-kaci-kechadi"],"blocksy_meta":[],"yoast_head":"\nTheoretical analysis of the excitations and instabilities of spinor dipolar Bose-Einstein condensates - 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\/2019\/11\/08\/theoretical-analysis-of-the-excitations-and-instabilities-of-spinor-dipolar-bose-einstein-condensates\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Theoretical analysis of the excitations and instabilities of spinor dipolar Bose-Einstein condensates - Magnetic Quantum Gases\" \/>\n<meta property=\"og:description\" content=\"French version: Analyse th\u00e9orique des excitations et des instabilit\u00e9s des condensats de Bose-Einstein spinoriels dipolaires Dans les condensats de Bose-Einstein spinoriels (CBES), plusieurs \u00e9tats de spin coexistent, donnant lieu \u00e0 des dynamiques pilot\u00e9es par des interactions d\u00e9pendantes du spin (interactions de contact (IC) et dip\u00f4le-dip\u00f4le (IDD)). En lien \u00e9troit avec les travaux exp\u00e9rimentaux de notre […]\" \/>\n<meta property=\"og:url\" content=\"https:\/\/gqm.lpl.univ-paris13.fr\/index.php\/2019\/11\/08\/theoretical-analysis-of-the-excitations-and-instabilities-of-spinor-dipolar-bose-einstein-condensates\/\" \/>\n<meta property=\"og:site_name\" content=\"Magnetic Quantum Gases\" \/>\n<meta property=\"article:published_time\" content=\"2019-11-08T13:32:00+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2025-10-28T14:23:38+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=\"4 minutes\" \/>\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\\\/2019\\\/11\\\/08\\\/theoretical-analysis-of-the-excitations-and-instabilities-of-spinor-dipolar-bose-einstein-condensates\\\/#article\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/gqm.lpl.univ-paris13.fr\\\/index.php\\\/2019\\\/11\\\/08\\\/theoretical-analysis-of-the-excitations-and-instabilities-of-spinor-dipolar-bose-einstein-condensates\\\/\"},\"author\":{\"name\":\"Benjamin PASQUIOU\",\"@id\":\"https:\\\/\\\/gqm.lpl.univ-paris13.fr\\\/#\\\/schema\\\/person\\\/edd1441f419c30858a44ed007fc1fc79\"},\"headline\":\"Theoretical analysis of the excitations and instabilities of spinor dipolar Bose-Einstein condensates\",\"datePublished\":\"2019-11-08T13:32:00+00:00\",\"dateModified\":\"2025-10-28T14:23:38+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\\\/\\\/gqm.lpl.univ-paris13.fr\\\/index.php\\\/2019\\\/11\\\/08\\\/theoretical-analysis-of-the-excitations-and-instabilities-of-spinor-dipolar-bose-einstein-condensates\\\/\"},\"wordCount\":750,\"publisher\":{\"@id\":\"https:\\\/\\\/gqm.lpl.univ-paris13.fr\\\/#organization\"},\"keywords\":[\"Kaci Kechadi\"],\"articleSection\":[\"PhD thesis\"],\"inLanguage\":\"en-US\"},{\"@type\":\"WebPage\",\"@id\":\"https:\\\/\\\/gqm.lpl.univ-paris13.fr\\\/index.php\\\/2019\\\/11\\\/08\\\/theoretical-analysis-of-the-excitations-and-instabilities-of-spinor-dipolar-bose-einstein-condensates\\\/\",\"url\":\"https:\\\/\\\/gqm.lpl.univ-paris13.fr\\\/index.php\\\/2019\\\/11\\\/08\\\/theoretical-analysis-of-the-excitations-and-instabilities-of-spinor-dipolar-bose-einstein-condensates\\\/\",\"name\":\"Theoretical analysis of the excitations and instabilities of spinor dipolar Bose-Einstein condensates - Magnetic Quantum Gases\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/gqm.lpl.univ-paris13.fr\\\/#website\"},\"datePublished\":\"2019-11-08T13:32:00+00:00\",\"dateModified\":\"2025-10-28T14:23:38+00:00\",\"breadcrumb\":{\"@id\":\"https:\\\/\\\/gqm.lpl.univ-paris13.fr\\\/index.php\\\/2019\\\/11\\\/08\\\/theoretical-analysis-of-the-excitations-and-instabilities-of-spinor-dipolar-bose-einstein-condensates\\\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\\\/\\\/gqm.lpl.univ-paris13.fr\\\/index.php\\\/2019\\\/11\\\/08\\\/theoretical-analysis-of-the-excitations-and-instabilities-of-spinor-dipolar-bose-einstein-condensates\\\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\\\/\\\/gqm.lpl.univ-paris13.fr\\\/index.php\\\/2019\\\/11\\\/08\\\/theoretical-analysis-of-the-excitations-and-instabilities-of-spinor-dipolar-bose-einstein-condensates\\\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\\\/\\\/gqm.lpl.univ-paris13.fr\\\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Theoretical analysis of the excitations and instabilities of spinor dipolar Bose-Einstein condensates\"}]},{\"@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":"Theoretical analysis of the excitations and instabilities of spinor dipolar Bose-Einstein condensates - 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\/2019\/11\/08\/theoretical-analysis-of-the-excitations-and-instabilities-of-spinor-dipolar-bose-einstein-condensates\/","og_locale":"en_US","og_type":"article","og_title":"Theoretical analysis of the excitations and instabilities of spinor dipolar Bose-Einstein condensates - Magnetic Quantum Gases","og_description":"French version: Analyse th\u00e9orique des excitations et des instabilit\u00e9s des condensats de Bose-Einstein spinoriels dipolaires Dans les condensats de Bose-Einstein spinoriels (CBES), plusieurs \u00e9tats de spin coexistent, donnant lieu \u00e0 des dynamiques pilot\u00e9es par des interactions d\u00e9pendantes du spin (interactions de contact (IC) et dip\u00f4le-dip\u00f4le (IDD)). En lien \u00e9troit avec les travaux exp\u00e9rimentaux de notre […]","og_url":"https:\/\/gqm.lpl.univ-paris13.fr\/index.php\/2019\/11\/08\/theoretical-analysis-of-the-excitations-and-instabilities-of-spinor-dipolar-bose-einstein-condensates\/","og_site_name":"Magnetic Quantum Gases","article_published_time":"2019-11-08T13:32:00+00:00","article_modified_time":"2025-10-28T14:23:38+00:00","author":"Benjamin PASQUIOU","twitter_misc":{"Written by":"Benjamin PASQUIOU","Est. reading time":"4 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"https:\/\/gqm.lpl.univ-paris13.fr\/index.php\/2019\/11\/08\/theoretical-analysis-of-the-excitations-and-instabilities-of-spinor-dipolar-bose-einstein-condensates\/#article","isPartOf":{"@id":"https:\/\/gqm.lpl.univ-paris13.fr\/index.php\/2019\/11\/08\/theoretical-analysis-of-the-excitations-and-instabilities-of-spinor-dipolar-bose-einstein-condensates\/"},"author":{"name":"Benjamin PASQUIOU","@id":"https:\/\/gqm.lpl.univ-paris13.fr\/#\/schema\/person\/edd1441f419c30858a44ed007fc1fc79"},"headline":"Theoretical analysis of the excitations and instabilities of spinor dipolar Bose-Einstein condensates","datePublished":"2019-11-08T13:32:00+00:00","dateModified":"2025-10-28T14:23:38+00:00","mainEntityOfPage":{"@id":"https:\/\/gqm.lpl.univ-paris13.fr\/index.php\/2019\/11\/08\/theoretical-analysis-of-the-excitations-and-instabilities-of-spinor-dipolar-bose-einstein-condensates\/"},"wordCount":750,"publisher":{"@id":"https:\/\/gqm.lpl.univ-paris13.fr\/#organization"},"keywords":["Kaci Kechadi"],"articleSection":["PhD thesis"],"inLanguage":"en-US"},{"@type":"WebPage","@id":"https:\/\/gqm.lpl.univ-paris13.fr\/index.php\/2019\/11\/08\/theoretical-analysis-of-the-excitations-and-instabilities-of-spinor-dipolar-bose-einstein-condensates\/","url":"https:\/\/gqm.lpl.univ-paris13.fr\/index.php\/2019\/11\/08\/theoretical-analysis-of-the-excitations-and-instabilities-of-spinor-dipolar-bose-einstein-condensates\/","name":"Theoretical analysis of the excitations and instabilities of spinor dipolar Bose-Einstein condensates - Magnetic Quantum Gases","isPartOf":{"@id":"https:\/\/gqm.lpl.univ-paris13.fr\/#website"},"datePublished":"2019-11-08T13:32:00+00:00","dateModified":"2025-10-28T14:23:38+00:00","breadcrumb":{"@id":"https:\/\/gqm.lpl.univ-paris13.fr\/index.php\/2019\/11\/08\/theoretical-analysis-of-the-excitations-and-instabilities-of-spinor-dipolar-bose-einstein-condensates\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/gqm.lpl.univ-paris13.fr\/index.php\/2019\/11\/08\/theoretical-analysis-of-the-excitations-and-instabilities-of-spinor-dipolar-bose-einstein-condensates\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/gqm.lpl.univ-paris13.fr\/index.php\/2019\/11\/08\/theoretical-analysis-of-the-excitations-and-instabilities-of-spinor-dipolar-bose-einstein-condensates\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/gqm.lpl.univ-paris13.fr\/"},{"@type":"ListItem","position":2,"name":"Theoretical analysis of the excitations and instabilities of spinor dipolar Bose-Einstein condensates"}]},{"@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\/"}]}},"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/gqm.lpl.univ-paris13.fr\/index.php\/wp-json\/wp\/v2\/posts\/597","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gqm.lpl.univ-paris13.fr\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gqm.lpl.univ-paris13.fr\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gqm.lpl.univ-paris13.fr\/index.php\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/gqm.lpl.univ-paris13.fr\/index.php\/wp-json\/wp\/v2\/comments?post=597"}],"version-history":[{"count":9,"href":"https:\/\/gqm.lpl.univ-paris13.fr\/index.php\/wp-json\/wp\/v2\/posts\/597\/revisions"}],"predecessor-version":[{"id":875,"href":"https:\/\/gqm.lpl.univ-paris13.fr\/index.php\/wp-json\/wp\/v2\/posts\/597\/revisions\/875"}],"wp:attachment":[{"href":"https:\/\/gqm.lpl.univ-paris13.fr\/index.php\/wp-json\/wp\/v2\/media?parent=597"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gqm.lpl.univ-paris13.fr\/index.php\/wp-json\/wp\/v2\/categories?post=597"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gqm.lpl.univ-paris13.fr\/index.php\/wp-json\/wp\/v2\/tags?post=597"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}