{"id":873,"date":"2024-07-01T15:14:49","date_gmt":"2024-07-01T15:14:49","guid":{"rendered":"https:\/\/www.matterwaveoptics.eu\/FOMO2024\/?p=873"},"modified":"2025-05-04T19:46:17","modified_gmt":"2025-05-04T19:46:17","slug":"towards-prime-factorisation-in-holographic-traps","status":"publish","type":"post","link":"https:\/\/www.matterwaveoptics.eu\/FOMO2024\/towards-prime-factorisation-in-holographic-traps\/","title":{"rendered":"Towards prime factorisation in holographic traps"},"content":{"rendered":"\n<p><span style=\"text-decoration: underline;\">Donatella Cassettari<\/span><\/p>\n\n\n\n<h1 class=\"wp-block-heading\">Abstract<\/h1>\n\n\n\n<p>We report the experimental realization of the prime number quantum potential V_N(x), defined as the potential entering the single-particle Schr\u00f6dinger Hamiltonian with eigenvalues given by the first N prime numbers. Using computer-generated holography, we create light intensity profiles suitable to optically trap ultracold atoms in these potentials for different N values. Our results pave the way toward the realization of quantum potentials with arbitrary sequences of integers as energy levels and show, in perspective, the possibility to set up quantum systems for arithmetic manipulations or mathematical tests involving prime numbers [1].<\/p>\n\n\n\n<p>[1] D. Cassettari, G. Mussardo and A. Trombettoni, Holographic realization of the prime number quantum potential, PNAS Nexus 2, Issue 1, pgac279 (2023).<\/p>\n\n\n\n<h1 class=\"wp-block-heading\">Video<\/h1>\n\n\n\n<figure class=\"wp-block-embed is-type-video is-provider-youtube wp-block-embed-youtube wp-embed-aspect-4-3 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<span class=\"embed-youtube\" style=\"text-align:center; display: block;\"><iframe loading=\"lazy\" class=\"youtube-player\" width=\"640\" height=\"360\" src=\"https:\/\/www.youtube.com\/embed\/Ch9kOoZyorQ?version=3&#038;rel=1&#038;showsearch=0&#038;showinfo=1&#038;iv_load_policy=1&#038;fs=1&#038;hl=en-US&#038;autohide=2&#038;wmode=transparent\" allowfullscreen=\"true\" style=\"border:0;\" sandbox=\"allow-scripts allow-same-origin allow-popups allow-presentation allow-popups-to-escape-sandbox\"><\/iframe><\/span>\n<\/div><\/figure>\n\n\n\n<h1 class=\"wp-block-heading\">Presentation<\/h1>\n\n\n\n<div data-wp-interactive=\"core\/file\" class=\"wp-block-file alignwide\"><object data-wp-bind--hidden=\"!state.hasPdfPreview\" hidden class=\"wp-block-file__embed\" data=\"https:\/\/www.matterwaveoptics.eu\/FOMO2024\/wp-content\/uploads\/2024\/07\/Donatella-Cassettari-Towards-prime-factorisation-in-holographic-traps.pdf\" type=\"application\/pdf\" style=\"width:100%;height:600px\" aria-label=\"Embed of Donatella Cassettari -- Towards prime factorisation in holographic traps.\"><\/object><a id=\"wp-block-file--media-cb5289e4-ce26-480c-ad51-b8f7acb41009\" href=\"https:\/\/www.matterwaveoptics.eu\/FOMO2024\/wp-content\/uploads\/2024\/07\/Donatella-Cassettari-Towards-prime-factorisation-in-holographic-traps.pdf\" target=\"_blank\" rel=\"noreferrer noopener\">Donatella Cassettari &#8212; Towards prime factorisation in holographic traps<\/a><a href=\"https:\/\/www.matterwaveoptics.eu\/FOMO2024\/wp-content\/uploads\/2024\/07\/Donatella-Cassettari-Towards-prime-factorisation-in-holographic-traps.pdf\" class=\"wp-block-file__button wp-element-button\" download aria-describedby=\"wp-block-file--media-cb5289e4-ce26-480c-ad51-b8f7acb41009\">Download<\/a><\/div>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h4 class=\"wp-block-heading\">Related Content:<\/h4>\n\n\n\n<div class=\"wp-block-query is-layout-flow wp-block-query-is-layout-flow\"><ul class=\"wp-block-post-template is-layout-flow wp-block-post-template-is-layout-flow\"><li class=\"wp-block-post post-141 post type-post status-publish format-standard has-post-thumbnail hentry category-invited-speaker tag-donatella-cassettari\">\n\n<div class=\"wp-block-columns are-vertically-aligned-center is-layout-flex wp-container-core-columns-is-layout-28f84493 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:25%\"><figure class=\"wp-block-post-featured-image\"><a href=\"https:\/\/www.matterwaveoptics.eu\/FOMO2024\/donatella-cassettari\/\" target=\"_self\"  ><img loading=\"lazy\" decoding=\"async\" width=\"254\" height=\"254\" src=\"https:\/\/www.matterwaveoptics.eu\/FOMO2024\/wp-content\/uploads\/2024\/04\/Donatella-Cassettari.jpeg\" class=\"attachment-post-thumbnail size-post-thumbnail wp-post-image\" alt=\"Donatella Cassettari\" style=\"object-fit:cover;\" srcset=\"https:\/\/www.matterwaveoptics.eu\/FOMO2024\/wp-content\/uploads\/2024\/04\/Donatella-Cassettari.jpeg 254w, https:\/\/www.matterwaveoptics.eu\/FOMO2024\/wp-content\/uploads\/2024\/04\/Donatella-Cassettari-150x150.jpeg 150w\" sizes=\"auto, (max-width: 254px) 100vw, 254px\" data-attachment-id=\"145\" data-permalink=\"https:\/\/www.matterwaveoptics.eu\/FOMO2024\/donatella-cassettari\/donatella-cassettari\/\" data-orig-file=\"https:\/\/www.matterwaveoptics.eu\/FOMO2024\/wp-content\/uploads\/2024\/04\/Donatella-Cassettari.jpeg\" data-orig-size=\"254,254\" data-comments-opened=\"0\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;1&quot;}\" data-image-title=\"Donatella-Cassettari\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.matterwaveoptics.eu\/FOMO2024\/wp-content\/uploads\/2024\/04\/Donatella-Cassettari.jpeg\" \/><\/a><\/figure><\/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:75%\">\n<div class=\"wp-block-group is-vertical is-layout-flex wp-container-core-group-is-layout-4b827052 wp-block-group-is-layout-flex\"><h2 class=\"wp-block-post-title has-large-font-size\"><a href=\"https:\/\/www.matterwaveoptics.eu\/FOMO2024\/donatella-cassettari\/\" target=\"_self\" >Donatella Cassettari<\/a><\/h2>\n\n<div style=\"text-decoration:underline\" class=\"taxonomy-category wp-block-post-terms\"><a href=\"https:\/\/www.matterwaveoptics.eu\/FOMO2024\/category\/conference\/speakers\/invited-speaker\/\" rel=\"tag\">Invited Speaker<\/a><\/div>\n\n<div style=\"text-decoration:underline\" class=\"taxonomy-post_tag wp-block-post-terms\"><a href=\"https:\/\/www.matterwaveoptics.eu\/FOMO2024\/tag\/donatella-cassettari\/\" rel=\"tag\">Cassettari, Donatella<\/a><\/div>\n\n<div class=\"wp-block-post-excerpt has-small-font-size\"><p class=\"wp-block-post-excerpt__excerpt\">University of St. Andrews <a class=\"wp-block-post-excerpt__more-link\" href=\"https:\/\/www.matterwaveoptics.eu\/FOMO2024\/donatella-cassettari\/\">(more)<\/a><\/p><\/div><\/div>\n<\/div>\n<\/div>\n\n<\/li><li class=\"wp-block-post post-873 post type-post status-publish format-standard has-post-thumbnail hentry category-presentation-videos category-invited-talk tag-donatella-cassettari\">\n\n<div class=\"wp-block-columns are-vertically-aligned-center is-layout-flex wp-container-core-columns-is-layout-28f84493 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:25%\"><figure class=\"wp-block-post-featured-image\"><a href=\"https:\/\/www.matterwaveoptics.eu\/FOMO2024\/towards-prime-factorisation-in-holographic-traps\/\" target=\"_self\"  ><img loading=\"lazy\" decoding=\"async\" width=\"904\" height=\"686\" src=\"https:\/\/www.matterwaveoptics.eu\/FOMO2024\/wp-content\/uploads\/2024\/07\/Cassettari-Towards-prime-factorisation-in-holographic-traps-1.jpg\" class=\"attachment-post-thumbnail size-post-thumbnail wp-post-image\" alt=\"Towards prime factorisation in holographic traps\" style=\"object-fit:cover;\" srcset=\"https:\/\/www.matterwaveoptics.eu\/FOMO2024\/wp-content\/uploads\/2024\/07\/Cassettari-Towards-prime-factorisation-in-holographic-traps-1.jpg 904w, https:\/\/www.matterwaveoptics.eu\/FOMO2024\/wp-content\/uploads\/2024\/07\/Cassettari-Towards-prime-factorisation-in-holographic-traps-1-300x228.jpg 300w, https:\/\/www.matterwaveoptics.eu\/FOMO2024\/wp-content\/uploads\/2024\/07\/Cassettari-Towards-prime-factorisation-in-holographic-traps-1-768x583.jpg 768w\" sizes=\"auto, (max-width: 904px) 100vw, 904px\" data-attachment-id=\"875\" data-permalink=\"https:\/\/www.matterwaveoptics.eu\/FOMO2024\/towards-prime-factorisation-in-holographic-traps\/cassettari-towards-prime-factorisation-in-holographic-traps-1\/\" data-orig-file=\"https:\/\/www.matterwaveoptics.eu\/FOMO2024\/wp-content\/uploads\/2024\/07\/Cassettari-Towards-prime-factorisation-in-holographic-traps-1.jpg\" data-orig-size=\"904,686\" data-comments-opened=\"0\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;1&quot;}\" data-image-title=\"Cassettari-Towards-prime-factorisation-in-holographic-traps-1\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.matterwaveoptics.eu\/FOMO2024\/wp-content\/uploads\/2024\/07\/Cassettari-Towards-prime-factorisation-in-holographic-traps-1.jpg\" \/><\/a><\/figure><\/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:75%\">\n<div class=\"wp-block-group is-vertical is-layout-flex wp-container-core-group-is-layout-4b827052 wp-block-group-is-layout-flex\"><h2 class=\"wp-block-post-title has-large-font-size\"><a href=\"https:\/\/www.matterwaveoptics.eu\/FOMO2024\/towards-prime-factorisation-in-holographic-traps\/\" target=\"_self\" >Towards prime factorisation in holographic traps<\/a><\/h2>\n\n<div style=\"text-decoration:underline\" class=\"taxonomy-category wp-block-post-terms\"><a href=\"https:\/\/www.matterwaveoptics.eu\/FOMO2024\/category\/conference\/presentation-videos\/\" rel=\"tag\">Conference Videos<\/a><span class=\"wp-block-post-terms__separator\">, <\/span><a href=\"https:\/\/www.matterwaveoptics.eu\/FOMO2024\/category\/conference\/talks\/invited-talk\/\" rel=\"tag\">Invited Talk<\/a><\/div>\n\n<div style=\"text-decoration:underline\" class=\"taxonomy-post_tag wp-block-post-terms\"><a href=\"https:\/\/www.matterwaveoptics.eu\/FOMO2024\/tag\/donatella-cassettari\/\" rel=\"tag\">Cassettari, Donatella<\/a><\/div>\n\n<div class=\"wp-block-post-excerpt has-small-font-size\"><p class=\"wp-block-post-excerpt__excerpt\">Donatella Cassettari Abstract We report the experimental realization of the prime number quantum potential V_N(x),&hellip; <a class=\"wp-block-post-excerpt__more-link\" href=\"https:\/\/www.matterwaveoptics.eu\/FOMO2024\/towards-prime-factorisation-in-holographic-traps\/\">(more)<\/a><\/p><\/div><\/div>\n<\/div>\n<\/div>\n\n<\/li><\/ul><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Donatella Cassettari Abstract We report the experimental realization of the prime number quantum potential V_N(x), defined as the potential entering the single-particle Schr\u00f6dinger Hamiltonian with eigenvalues given by the first N prime numbers. Using computer-generated holography, we create light intensity profiles suitable to optically trap ultracold atoms in these potentials for different N values. Our [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":875,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"advanced_seo_description":"","jetpack_seo_html_title":"","jetpack_seo_noindex":false,"jetpack_post_was_ever_published":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":true,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2}},"categories":[186,52],"tags":[27],"class_list":["post-873","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-presentation-videos","category-invited-talk","tag-donatella-cassettari"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"https:\/\/www.matterwaveoptics.eu\/FOMO2024\/wp-content\/uploads\/2024\/07\/Cassettari-Towards-prime-factorisation-in-holographic-traps-1.jpg","jetpack-related-posts":[{"id":141,"url":"https:\/\/www.matterwaveoptics.eu\/FOMO2024\/donatella-cassettari\/","url_meta":{"origin":873,"position":0},"title":"Donatella Cassettari","author":"wvk_3vn943","date":"April 9, 2024","format":false,"excerpt":"University of St. Andrews Donatella Cassettari is a Lecturer in Quantum Phenomena at the University of St. Andrews. Her research programme focuses on holographic optical traps for ultracold atoms. Holographic traps are realised by shaping the intensity profile of a laser beam using a spatial light modulator, and they allow\u2026","rel":"","context":"In &quot;Invited Speaker&quot;","block_context":{"text":"Invited Speaker","link":"https:\/\/www.matterwaveoptics.eu\/FOMO2024\/category\/conference\/speakers\/invited-speaker\/"},"img":{"alt_text":"","src":"https:\/\/i0.wp.com\/www.matterwaveoptics.eu\/FOMO2024\/wp-content\/uploads\/2024\/04\/Donatella-Cassettari.jpeg?resize=350%2C200&ssl=1","width":350,"height":200},"classes":[]},{"id":1697,"url":"https:\/\/www.matterwaveoptics.eu\/FOMO2024\/programme-for-monday-9-september\/","url_meta":{"origin":873,"position":1},"title":"Monday 9 September: Conference Programme","author":"wvk_3vn943","date":"September 9, 2024","format":false,"excerpt":"Welcome by Wolf von Klitzing Monday 9 September 2024, 09:15\u2009\u2013\u200909:30 KEYNOTE by Markus Arndt Monday 9 September 2024, 09:30\u2009\u2013\u200910:15 Universal matter-wave interferometry across the mass & complexity scales Contributed Monday 9 September 2024, 10:16\u2009\u2013\u200910:46 FATTORI MARCO: Differential Mach-Zehnder interferometry with trapped Bose Einstein condensates Contributed Monday 9 September 2024, 10:45\u2009\u2013\u200911:15\u2026","rel":"","context":"In &quot;Programmes&quot;","block_context":{"text":"Programmes","link":"https:\/\/www.matterwaveoptics.eu\/FOMO2024\/category\/conference\/programmes\/"},"img":{"alt_text":"","src":"https:\/\/i0.wp.com\/www.matterwaveoptics.eu\/FOMO2024\/wp-content\/uploads\/2024\/09\/ScreenShotXXX-6.png?resize=350%2C200&ssl=1","width":350,"height":200},"classes":[]},{"id":116,"url":"https:\/\/www.matterwaveoptics.eu\/FOMO2024\/carrie-weidner\/","url_meta":{"origin":873,"position":2},"title":"Carrie Weidner","author":"wvk_3vn943","date":"April 9, 2024","format":false,"excerpt":"Lecturer in Quantum Engineering at the University of Bristol Dr Carrie Weidner is a Lecturer in the Quantum Engineering Technology Laboratories at the University of Bristol, UK, where she leads a research group concerned with the control and manipulation of quantum systems Weidner did her PhD in JILA at the\u2026","rel":"","context":"In &quot;Invited Speaker&quot;","block_context":{"text":"Invited Speaker","link":"https:\/\/www.matterwaveoptics.eu\/FOMO2024\/category\/conference\/speakers\/invited-speaker\/"},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":825,"url":"https:\/\/www.matterwaveoptics.eu\/FOMO2024\/controlling-ultracold-atoms-in-optical-lattices-theory-and-practice-but-mostly-practice\/","url_meta":{"origin":873,"position":3},"title":"Controlling ultracold atoms in optical lattices: theory and practice (but mostly practice)","author":"wvk_3vn943","date":"June 24, 2024","format":false,"excerpt":"Quantum optimal control is a fantastic means of manipulating quantum systems for the purposes of quantum technology. In this realm, my specific interests for the past decade have centered around the (largely experimental) quantum control of very cold atoms in the sinusoidal potentials offered by optical lattice potentials. 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