CINXE.COM

entanglement – Department of Physics – UW–Madison

<!DOCTYPE html> <html lang="en-US" prefix="og: http://ogp.me/ns# fb: http://ogp.me/ns/fb#" class="no-js"> <head> <meta http-equiv="X-UA-Compatible" content="IE=edge"> <meta charset="UTF-8"> <meta name="viewport" content="width=device-width, initial-scale=1"> <link rel="preload" href="https://www.physics.wisc.edu/wp-content/themes/uw-theme/dist/fonts/uw-rh/redhat-display-latin.v14.woff2" as="font" type="font/woff2" crossorigin> <link rel="preload" href="https://www.physics.wisc.edu/wp-content/themes/uw-theme/dist/fonts/uw-rh/redhat-text-latin.v13.woff2" as="font" type="font/woff2" crossorigin> <!-- Global site tag (gtag.js) - Google Analytics --> <script async src="https://www.googletagmanager.com/gtag/js?id=G-HDEG1JB5JH"></script> <script> window.dataLayer = window.dataLayer || []; function gtag(){dataLayer.push(arguments);} gtag('js', new Date()); gtag('config', 'G-HDEG1JB5JH', { 'cookie_domain': 'none' }); </script> <script>(function(H){H.className=H.className.replace(/\bno-js\b/,'')})(document.documentElement)</script> <title>entanglement &#8211; Department of Physics &#8211; UW–Madison</title> <meta name='robots' content='max-image-preview:large' /> <style>img:is([sizes="auto" i], [sizes^="auto," i]) { contain-intrinsic-size: 3000px 1500px }</style> <link rel='dns-prefetch' href='//cdn.wisc.cloud' /> <link rel="alternate" type="application/rss+xml" title="Department of Physics &raquo; Feed" href="https://www.physics.wisc.edu/feed/" /> <link rel="alternate" type="application/rss+xml" title="Department of Physics &raquo; Comments Feed" href="https://www.physics.wisc.edu/comments/feed/" /> <link rel="alternate" type="application/rss+xml" title="Department of Physics &raquo; entanglement Tag Feed" href="https://www.physics.wisc.edu/tag/entanglement/feed/" /> <link rel='stylesheet' id='sbi_styles-css' href='https://www.physics.wisc.edu/wp-content/plugins/instagram-feed/css/sbi-styles.min.css?ver=6.6.1' media='all' /> <style id='classic-theme-styles-inline-css'> /*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} </style> <link rel='stylesheet' id='bg-shce-genericons-css' href='https://www.physics.wisc.edu/wp-content/plugins/show-hidecollapse-expand/assets/css/genericons/genericons.css?ver=6.7.1' media='all' /> <link rel='stylesheet' id='bg-show-hide-css' href='https://www.physics.wisc.edu/wp-content/plugins/show-hidecollapse-expand/assets/css/bg-show-hide.css?ver=6.7.1' media='all' /> <link rel='stylesheet' id='parent-style-css' href='https://www.physics.wisc.edu/wp-content/themes/uw-theme/style.css?ver=6.7.1' media='all' /> <link rel='stylesheet' id='child-style-css' href='https://www.physics.wisc.edu/wp-content/themes/uw-physics/style.css?ver=1.0.4' media='all' /> <link rel='stylesheet' id='uwmadison-style-css' href='https://www.physics.wisc.edu/wp-content/themes/uw-theme/dist/main.min.css?ver=1.35.1' media='all' /> <!--[if lt IE 10]> <link rel='stylesheet' id='uwmadison-ie-css' href='https://www.physics.wisc.edu/wp-content/themes/uw-theme/dist/css/ie.css?ver=1.35.1' media='all' /> <![endif]--> <link rel="https://api.w.org/" href="https://www.physics.wisc.edu/wp-json/" /><link rel="alternate" title="JSON" type="application/json" href="https://www.physics.wisc.edu/wp-json/wp/v2/tags/293" /><link rel="EditURI" type="application/rsd+xml" title="RSD" href="https://www.physics.wisc.edu/xmlrpc.php?rsd" /> <!-- Generic meta tags --> <meta name="description" content="Research, teaching and outreach in Physics at UW–Madison" /> <!-- Open Graph meta tags --> <meta property="og:title" content="entanglement" /> <meta property="og:url" content="https://www.physics.wisc.edu/2024/06/06/entangled-neutrinos-may-lead-to-heavier-element-formation/" /> <meta property="og:description" content="Research, teaching and outreach in Physics at UW–Madison" /> <meta property="og:site_name" content="Department of Physics" /> <meta property="og:type" content="website" /> <meta property="og:image" content="https://www.physics.wisc.edu/wp-content/uploads/2024/06/i-process-APJ-figure-13-entangled-neutrinos-1024x746.jpeg" /> <meta property="og:image:alt" content ="a plot of mass number A (atomic number) on the x-axis and abundance as a log scale on the y-axis. a purple line shows the i-process abundance, black line shows r-process, and grey line shows s-process. Above atomic number 140 or so, there is a visible enhancement of the purple line over the other two lines (below 140 the black and grey lines are much higher abundance values than the purple line)" /> <meta property="og:image:height" content="466"/> <meta property="og:image:width" content="640"/> <!-- Schema.org meta tags --> <meta itemprop="name" content="entanglement"> <meta itemprop="description" content="Research, teaching and outreach in Physics at UW–Madison"> <meta itemprop="image" content="https://www.physics.wisc.edu/wp-content/uploads/2024/06/i-process-APJ-figure-13-entangled-neutrinos-1024x746.jpeg"> <!-- Twitter meta tags --> <meta name="twitter:card" content="summary" /> <meta name="twitter:title" content="entanglement" /> <meta name="twitter:description" content="Research, teaching and outreach in Physics at UW–Madison" /> <meta property="twitter:image" content="https://www.physics.wisc.edu/wp-content/uploads/2024/06/i-process-APJ-figure-13-entangled-neutrinos-1024x746.jpeg" /> <meta property="twitter:image:src" content="https://www.physics.wisc.edu/wp-content/uploads/2024/06/i-process-APJ-figure-13-entangled-neutrinos-1024x746.jpeg" /> <meta property="twitter:image:alt" content ="a plot of mass number A (atomic number) on the x-axis and abundance as a log scale on the y-axis. a purple line shows the i-process abundance, black line shows r-process, and grey line shows s-process. Above atomic number 140 or so, there is a visible enhancement of the purple line over the other two lines (below 140 the black and grey lines are much higher abundance values than the purple line)" /> <!-- START - Open Graph and Twitter Card Tags 3.3.3 --> <!-- Facebook Open Graph --> <meta property="og:locale" content="en_US"/> <meta property="og:site_name" content="Department of Physics"/> <meta property="og:title" content="entanglement"/> <meta property="og:url" content="https://www.physics.wisc.edu/tag/entanglement/"/> <meta property="og:type" content="article"/> <meta property="og:description" content="Research, teaching and outreach in Physics at UW–Madison"/> <!-- Google+ / Schema.org --> <meta itemprop="name" content="entanglement"/> <meta itemprop="headline" content="entanglement"/> <meta itemprop="description" content="Research, teaching and outreach in Physics at UW–Madison"/> <!--<meta itemprop="publisher" content="Department of Physics"/>--> <!-- To solve: The attribute publisher.itemtype has an invalid value --> <!-- Twitter Cards --> <meta name="twitter:title" content="entanglement"/> <meta name="twitter:url" content="https://www.physics.wisc.edu/tag/entanglement/"/> <meta name="twitter:description" content="Research, teaching and outreach in Physics at UW–Madison"/> <meta name="twitter:card" content="summary_large_image"/> <!-- SEO --> <!-- Misc. tags --> <!-- is_tag --> <!-- END - Open Graph and Twitter Card Tags 3.3.3 --> <link rel="profile" href="http://gmpg.org/xfn/11"> <link rel="apple-touch-icon" href="https://www.physics.wisc.edu/wp-content/themes/uw-theme/dist/images/favicons/apple-touch-icon.png"> <link rel="icon" type="image/png" sizes="32x32" href="https://www.physics.wisc.edu/wp-content/themes/uw-theme/dist/images/favicons/favicon-32x32.png"> <link rel="icon" type="image/png" sizes="16x16" href="https://www.physics.wisc.edu/wp-content/themes/uw-theme/dist/images/favicons/favicon-16x16.png"> <link rel="manifest" href="https://www.physics.wisc.edu/wp-content/themes/uw-theme/dist/images/favicons/site.webmanifest"> <link rel="mask-icon" href="https://www.physics.wisc.edu/wp-content/themes/uw-theme/dist/images/favicons/safari-pinned-tab.svg" color="#c5050c"> <link rel="icon" href="/favicon.ico"> <meta name="msapplication-TileColor" content="#c5050c"> <meta name="msapplication-config" content="https://www.physics.wisc.edu/wp-content/themes/uw-theme/dist/images/favicons/browserconfig.xml"> <meta name="theme-color" content="#ffffff"> </head> <body class="archive tag tag-entanglement tag-293 uw-white-bg"> <a class="show-on-focus" href="#main" id="skip-link">Skip to main content</a> <div class="uw-global-bar " role="navigation"> <a class="uw-global-name-link" href="https://www.wisc.edu" aria-label="University of Wisconsin Madison home page">U<span>niversity <span class="uw-of">of</span> </span>W<span>isconsin</span>–Madison</a> </div> <header class="uw-header uw-has-search"> <div class="uw-header-container"> <div class="uw-header-crest-title"> <div class="uw-header-crest"> <a href="https://www.physics.wisc.edu/" aria-hidden="true" tabindex="-1"><svg viewBox="0 0 55.5 87.28" version="1.1" role="img" focusable="false" aria-hidden="true" aria-labelledby="dynid67501fbec8f373.19027286"> <title id="dynid67501fbec8f373.19027286">UW Crest</title> <style> .cls-1{fill:url(#Web_Shield_blend);} .cls-2{fill:#282728;} .cls-3{fill:#c5050c;} .cls-4{fill:#fff;} </style> <g> <radialGradient id="Web_Shield_blend" cx="46.25" cy="16.57" r="33.44" gradientTransform="translate(-22.22 26.01) scale(1.09 1.09)" gradientUnits="userSpaceOnUse"><stop offset="0.17" stop-color="#fff"/><stop offset="0.3" stop-color="#f6ede4"/><stop offset="0.69" stop-color="#debe9b"/><stop offset="0.87" stop-color="#d4ac7f"/></radialGradient> </g> <path id="Gold_gradient" data-name="Gold gradient" class="cls-1" d="M28,87.36a3.78,3.78,0,0,1-1.05-1.16l-0.06-.09-0.11,0C8.65,81.86-1.45,54,.83,31.71a47.71,47.71,0,0,1,1.29-7.25,35.39,35.39,0,0,1,2.33-6.39,23.55,23.55,0,0,1,3.75-5.65A14.7,14.7,0,0,1,19,7.28,0.33,0.33,0,0,0,19.33,7,5.49,5.49,0,0,1,23.21,4.4l0.19,0,0-.19A4.69,4.69,0,0,1,28,.64a4.76,4.76,0,0,1,4.56,3.54l0,0.19,0.19,0A5.51,5.51,0,0,1,36.67,7a0.32,0.32,0,0,0,.37.26,14.7,14.7,0,0,1,10.77,5.13,24,24,0,0,1,4.24,6.71l0.23,0.55a42.56,42.56,0,0,1,2.89,12C57.45,54,47.35,81.86,29.23,86.08l-0.11,0-0.06.09A3.78,3.78,0,0,1,28,87.36Z" transform="translate(-0.25 -0.36)"/><path id="Black" class="cls-2" d="M55.43,31.68a49.49,49.49,0,0,0-.86-5.5,39.81,39.81,0,0,0-1.39-4.93,31.29,31.29,0,0,0-2.23-4.93,22.63,22.63,0,0,0-3-4.1A14.94,14.94,0,0,0,37,7H36.94a5.77,5.77,0,0,0-4.16-2.91,4.93,4.93,0,0,0-9.56,0A5.77,5.77,0,0,0,19.06,7H19A14.94,14.94,0,0,0,8,12.23a22.63,22.63,0,0,0-3,4.1,31.29,31.29,0,0,0-2.23,4.93,39.81,39.81,0,0,0-1.39,4.93,49.49,49.49,0,0,0-.86,5.5C-1.73,54.3,8.44,82.1,26.73,86.36A3.17,3.17,0,0,0,28,87.64a3.17,3.17,0,0,0,1.27-1.28C47.56,82.1,57.73,54.3,55.43,31.68ZM28,1.23A3.9,3.9,0,0,1,31.93,4a4.86,4.86,0,0,0-3.86,2.47,0.17,0.17,0,0,1-.07.09,0.15,0.15,0,0,1-.07-0.09A4.86,4.86,0,0,0,24.07,4,3.9,3.9,0,0,1,28,1.23ZM26.14,5.52a3.51,3.51,0,0,1,1.59,2.11A0.46,0.46,0,0,0,28,8a0.46,0.46,0,0,0,.27-0.42,3.51,3.51,0,0,1,1.59-2.11,4.19,4.19,0,0,1,6,1.58,13.38,13.38,0,0,0-1.67.42,6.6,6.6,0,0,0-2.38,1.32,9.4,9.4,0,0,0-3,6.1c-0.67,7.31,7.72,6.16,8.14,6.13,1.08,0,1.9-1.71,1.9-4s-0.84-4-1.9-4c-0.65,0-1.77.52-1.88,2.55C35,17.1,35.7,19,36.6,19.11c0.47,0.06.89-.76,1-1.6s0.06-1.87-.59-2a0.38,0.38,0,0,0-.46.28A3.83,3.83,0,0,1,37,17.1c0,1.25-1.28.63-1.12-1.36C36,14,36.89,14.09,36.93,14.09c0.5,0,1.26,1,1.26,3,0,1.75-.84,3.63-2.46,2.65-1.36-1-1.89-3.28-1.52-5,0.17-.81.87-3,3.13-3,3.26,0,6.3,1.71,8.72,4.9-0.27.85-1.95,4.1-7.28,7.21l-0.29.15a11,11,0,0,0-4.93-1,27.07,27.07,0,0,0-4.64.74,4.09,4.09,0,0,1-.92.15h0a4.09,4.09,0,0,1-.92-0.15A27.07,27.07,0,0,0,22.44,23a11,11,0,0,0-4.93,1l-0.29-.15c-5.34-3.11-7-6.36-7.28-7.21,2.42-3.19,5.46-4.9,8.72-4.9,2.26,0,3,2.21,3.13,3,0.38,1.77-.16,4.05-1.52,5-1.61,1-2.46-.9-2.46-2.65,0-2,.76-3,1.26-3,0,0,.94-0.11,1.09,1.65,0.17,2-1.09,2.61-1.12,1.36a3.83,3.83,0,0,1,.39-1.34A0.38,0.38,0,0,0,19,15.48c-0.65.16-.71,1.3-0.59,2s0.56,1.66,1,1.6c0.9-.12,1.6-2,1.52-3.44-0.1-2-1.23-2.55-1.88-2.55-1.06,0-1.9,1.71-1.9,4s0.82,4,1.9,4c0.42,0,8.81,1.18,8.14-6.13a9.4,9.4,0,0,0-3-6.1,6.6,6.6,0,0,0-2.38-1.32A13.38,13.38,0,0,0,20.1,7.1,4.19,4.19,0,0,1,26.14,5.52ZM10.28,36.18A32.49,32.49,0,0,0,10,39.49a44.42,44.42,0,0,0,2,15.25,49.48,49.48,0,0,0,4.13,9.32A11.48,11.48,0,0,1,11,66.39,66.66,66.66,0,0,1,4.53,34.57,16.13,16.13,0,0,0,10.28,36.18ZM4.56,34c0.44-7.31,2.29-13.05,5-16.87,0.48,1.24,2.57,4.35,7.39,7.18-4.1,2.47-6,7.56-6.58,11.36A15.81,15.81,0,0,1,4.56,34ZM16.41,64.53c3.08,5.3,6.12,8.46,8.45,10.13A11.54,11.54,0,0,1,21.32,79c-4-2.7-7.4-7-10.07-12.13A11.81,11.81,0,0,0,16.41,64.53ZM25.33,75A12.2,12.2,0,0,0,28,76.46,12.2,12.2,0,0,0,30.67,75a12,12,0,0,0,3.53,4.34,18.69,18.69,0,0,1-3.58,1.78s0-.09,0-0.13c-0.26-1.32-2-1.59-2.61-1.59s-2.35.27-2.61,1.59c0,0,0,.09,0,0.13a18.69,18.69,0,0,1-3.58-1.78A12,12,0,0,0,25.33,75Zm5.81-.32c2.33-1.67,5.37-4.83,8.45-10.13a11.81,11.81,0,0,0,5.16,2.36C42.08,72,38.69,76.32,34.68,79A11.54,11.54,0,0,1,31.14,74.66Zm8.72-10.61A49.48,49.48,0,0,0,44,54.73a44.1,44.1,0,0,0,1.66-7.32A44.34,44.34,0,0,0,46,39.49a32.49,32.49,0,0,0-.32-3.31,16.13,16.13,0,0,0,5.75-1.61A66.66,66.66,0,0,1,45,66.39,11.48,11.48,0,0,1,39.86,64.05Zm5.78-28.4c-0.62-3.8-2.5-8.8-6.58-11.36,4.82-2.83,6.92-5.94,7.39-7.18,2.69,3.82,4.55,9.56,5,16.87A15.81,15.81,0,0,1,45.64,35.65ZM25,84.76a23.29,23.29,0,0,1-5.87-2.93,27.5,27.5,0,0,1-3.25-2.62,31.1,31.1,0,0,1-2.35-2.47q-0.76-.88-1.46-1.81a47.49,47.49,0,0,1-5.58-9.69A63.9,63.9,0,0,1,3.09,55,70.46,70.46,0,0,1,1.3,44.19a64.57,64.57,0,0,1-.07-10.84C1.4,31.43,1.63,29.5,2,27.59A39.32,39.32,0,0,1,3.4,22a31,31,0,0,1,2.1-4.86,20.93,20.93,0,0,1,3.15-4.44,16.19,16.19,0,0,1,4-3.1,13.93,13.93,0,0,1,1.93-.87q0.51-.18,1-0.32a8.82,8.82,0,0,1,1-.26,14,14,0,0,1,2.56-.21,7.58,7.58,0,0,1,3.88,1,8,8,0,0,1,3.34,6c0.39,4.52-4.21,5.23-5.11,5.22-0.14,0-.21-0.13.24-0.59a6.53,6.53,0,0,0,1-5.1c-0.44-2.07-1.9-3.69-4-3.69a11.16,11.16,0,0,0-8.12,3.89A22.78,22.78,0,0,0,6,22.61,42.69,42.69,0,0,0,3.76,34,62.43,62.43,0,0,0,4,44.63,68.71,68.71,0,0,0,5.94,55.22a60.82,60.82,0,0,0,3.53,9.85,43.36,43.36,0,0,0,5.48,9A25.89,25.89,0,0,0,23.08,81a18.15,18.15,0,0,0,2.21,1A6.71,6.71,0,0,0,26,85,6.63,6.63,0,0,1,25,84.76Zm3.29,1.55a0.6,0.6,0,0,1-.31.21,0.6,0.6,0,0,1-.31-0.21,6.49,6.49,0,0,1-1.51-5.17c0.12-.64,1.2-0.93,1.82-0.94s1.7,0.3,1.82.94A6.49,6.49,0,0,1,28.31,86.3ZM54.7,44.19A70.46,70.46,0,0,1,52.91,55a63.9,63.9,0,0,1-3.42,10.2,47.49,47.49,0,0,1-5.58,9.69q-0.7.93-1.46,1.81a31.1,31.1,0,0,1-2.35,2.47,27.5,27.5,0,0,1-3.25,2.62A23.29,23.29,0,0,1,31,84.76,6.63,6.63,0,0,1,30,85a6.71,6.71,0,0,0,.67-3.1,18.15,18.15,0,0,0,2.21-1,25.89,25.89,0,0,0,8.13-6.87,43.36,43.36,0,0,0,5.48-9,60.82,60.82,0,0,0,3.53-9.85A68.71,68.71,0,0,0,52,44.63,62.43,62.43,0,0,0,52.24,34,42.69,42.69,0,0,0,50,22.61a22.78,22.78,0,0,0-4.47-7.87,11.16,11.16,0,0,0-8.12-3.89c-2.12,0-3.58,1.62-4,3.69a6.53,6.53,0,0,0,1,5.1c0.45,0.46.38,0.59,0.24,0.59-0.9,0-5.51-.71-5.11-5.22a8,8,0,0,1,3.34-6,7.58,7.58,0,0,1,3.88-1,14,14,0,0,1,2.56.21,8.77,8.77,0,0,1,1,.26q0.52,0.14,1,.32a13.93,13.93,0,0,1,1.93.87,16.19,16.19,0,0,1,4,3.1,20.93,20.93,0,0,1,3.15,4.44A31,31,0,0,1,52.6,22,39.32,39.32,0,0,1,54,27.59c0.35,1.91.58,3.84,0.74,5.77A64.57,64.57,0,0,1,54.7,44.19Z" transform="translate(-0.25 -0.36)"/><path id="Red" class="cls-3" d="M45,39.63c-0.11-2.69-.9-10.9-6.48-14.46A9.41,9.41,0,0,0,34.18,24c-2.74-.18-4.77.87-6.14,0.91H28c-1.37,0-3.42-1.09-6.16-.91a9.35,9.35,0,0,0-4.37,1.21C11.85,28.73,11.07,36.94,11,39.63a43.52,43.52,0,0,0,3.54,19C18.36,67.12,23,73.14,27.63,75.19L28,75.35l0.37-.16c4.61-2,9.27-8.06,13.14-16.57A43.53,43.53,0,0,0,45,39.63Z" transform="translate(-0.25 -0.36)"/><path id="W" class="cls-4" d="M36.3,33.18V35L36.67,35h0.18a1.17,1.17,0,0,1,.82.28,1.27,1.27,0,0,1,.21,1.11s-3.74,16.19-4.45,19.27c-0.82-3.9-5.26-25.18-5.26-25.18l0-.09H27.27v0.1L23.4,55.32,19,36.37a2.7,2.7,0,0,1,0-.28,1.27,1.27,0,0,1,.31-1A1,1,0,0,1,20,34.92l0.37,0v-1.8H14.13v1.76l0.28,0a1.16,1.16,0,0,1,.95.83L23,68.48l0,0.09h1.1v-0.1l3.56-23.3,4.53,23.31,0,0.09h1l7.25-32.78a1,1,0,0,1,1-.75h0.07l0.36,0V33.18H36.3Z" transform="translate(-0.25 -0.36)"/> </svg></a> </div> <div class="uw-title-tagline"> <div id="site-title" class="uw-site-title uw-red-title "> <a href="https://www.physics.wisc.edu/" rel="home">Department of Physics</a> </div> <div id="site-description" class="uw-site-tagline">Research, teaching and outreach in Physics at UW–Madison</div> </div> </div> <div class="uw-header-search"> <form role="search" class="uw-search-form" method="get" id="searchform" action="https://www.physics.wisc.edu/"> <label for="s" class="show-for-sr">Search</label> <input type="text" class="field uw-search-input" name="s" id="s" placeholder="Search" /> <input type="submit" class="submit uw-search-submit uw-button" name="submit" id="searchsubmit" value="Search" /> </form> </div> </div> </header><!-- #branding --> <button class="uw-mobile-menu-button-bar uw-mobile-menu-button-bar-reversed" aria-label="Open menu" aria-expanded="false" aria-controls="uw-top-menus"><span>Menu</span><svg viewBox="0 0 1024 1024" version="1.1" role="img" focusable="false" aria-labelledby="dynid67501fbec940c1.92184568"> <title id="dynid67501fbec940c1.92184568">open menu</title> <path class="path1" d="M128 256h768v86h-768v-86zM128 554v-84h768v84h-768zM128 768v-86h768v86h-768z"/> </svg><svg viewBox="0 0 805 1024" version="1.1" role="img" focusable="false" aria-labelledby="dynid67501fbec94b15.56941504"> <title id="dynid67501fbec94b15.56941504">close</title> <path class="path1" d="M741.714 755.429q0 22.857-16 38.857l-77.714 77.714q-16 16-38.857 16t-38.857-16l-168-168-168 168q-16 16-38.857 16t-38.857-16l-77.714-77.714q-16-16-16-38.857t16-38.857l168-168-168-168q-16-16-16-38.857t16-38.857l77.714-77.714q16-16 38.857-16t38.857 16l168 168 168-168q16-16 38.857-16t38.857 16l77.714 77.714q16 16 16 38.857t-16 38.857l-168 168 168 168q16 16 16 38.857z"/> </svg></button> <div id="uw-top-menus" class="uw-is-visible uw-horizontal uw-hidden" aria-hidden="false"> <div class="uw-main-nav"> <nav class="uw-nav-menu uw-nav-menu-reverse" aria-label="Main Menu"> <ul id="uw-main-nav" class=""><li id="menu-item-3698" class="menu-item menu-item-type-post_type menu-item-object-page menu-item-has-children uw-dropdown menu-item-3698"><a href="https://www.physics.wisc.edu/graduate/" aria-haspopup="true" aria-expanded="false">Graduate<svg class="uw-caret" viewBox="0 0 1792 1792" version="1.1" role="img" focusable="false" aria-hidden="true" aria-labelledby="dynid67501fbee07f50.12033147"> <title id="dynid67501fbee07f50.12033147">Expand</title> <path d="M1395 736q0 13-10 23l-466 466q-10 10-23 10t-23-10l-466-466q-10-10-10-23t10-23l50-50q10-10 23-10t23 10l393 393 393-393q10-10 23-10t23 10l50 50q10 10 10 23z"/> </svg><svg class="uw-caret" viewBox="0 0 1792 1792" version="1.1" role="img" focusable="false" aria-hidden="true" aria-labelledby="dynid67501fbee08bd6.51315674"> <title id="dynid67501fbee08bd6.51315674">Collapse</title> <path d="M1395 1184q0 13-10 23l-50 50q-10 10-23 10t-23-10l-393-393-393 393q-10 10-23 10t-23-10l-50-50q-10-10-10-23t10-23l466-466q10-10 23-10t23 10l466 466q10 10 10 23z"/> </svg></a> <ul aria-hidden="true" aria-label="Graduate submenu" class="sub-menu uw-child-menu"> <li id="menu-item-3701" class="menu-item menu-item-type-post_type menu-item-object-page menu-item-3701"><a href="https://www.physics.wisc.edu/graduate/">Prospective Students</a></li> <li id="menu-item-12558" class="menu-item menu-item-type-post_type menu-item-object-page menu-item-12558"><a href="https://www.physics.wisc.edu/graduate/phd-program/">PhD Program</a></li> <li id="menu-item-8556" class="menu-item menu-item-type-post_type menu-item-object-page menu-item-8556"><a href="https://www.physics.wisc.edu/graduate/mspqc-program/">MSPQC Program</a></li> <li id="menu-item-7973" class="menu-item menu-item-type-custom menu-item-object-custom menu-item-7973"><a href="https://www.physics.wisc.edu/courses/">Courses</a></li> <li id="menu-item-7974" class="menu-item menu-item-type-post_type menu-item-object-page menu-item-7974"><a href="https://www.physics.wisc.edu/uw-student-resources/">Student Resources</a></li> <li id="menu-item-7975" class="menu-item menu-item-type-post_type menu-item-object-page menu-item-7975"><a href="https://www.physics.wisc.edu/graduate/phd-program/contacts/">PhD Program Contacts</a></li> <li id="menu-item-7976" class="menu-item menu-item-type-post_type menu-item-object-page menu-item-7976"><a href="https://www.physics.wisc.edu/graduate/mspqc-current-students/mspqc-faculty/">MSPQC Program Contacts</a></li> </ul> </li> <li id="menu-item-3188" class="menu-item menu-item-type-custom menu-item-object-custom menu-item-has-children uw-dropdown menu-item-3188"><a href="https://www.physics.wisc.edu/undergraduate/" aria-haspopup="true" aria-expanded="false">Undergraduate<svg class="uw-caret" viewBox="0 0 1792 1792" version="1.1" role="img" focusable="false" aria-hidden="true" aria-labelledby="dynid67501fbee0c193.04296296"> <title id="dynid67501fbee0c193.04296296">Expand</title> <path d="M1395 736q0 13-10 23l-466 466q-10 10-23 10t-23-10l-466-466q-10-10-10-23t10-23l50-50q10-10 23-10t23 10l393 393 393-393q10-10 23-10t23 10l50 50q10 10 10 23z"/> </svg><svg class="uw-caret" viewBox="0 0 1792 1792" version="1.1" role="img" focusable="false" aria-hidden="true" aria-labelledby="dynid67501fbee0cbf7.20451301"> <title id="dynid67501fbee0cbf7.20451301">Collapse</title> <path d="M1395 1184q0 13-10 23l-50 50q-10 10-23 10t-23-10l-393-393-393 393q-10 10-23 10t-23-10l-50-50q-10-10-10-23t10-23l466-466q10-10 23-10t23 10l466 466q10 10 10 23z"/> </svg></a> <ul aria-hidden="true" aria-label="Undergraduate submenu" class="sub-menu uw-child-menu"> <li id="menu-item-9666" class="menu-item menu-item-type-post_type menu-item-object-page menu-item-9666"><a href="https://www.physics.wisc.edu/undergraduate/">Home</a></li> <li id="menu-item-7981" class="menu-item menu-item-type-post_type menu-item-object-page menu-item-7981"><a href="https://www.physics.wisc.edu/undergraduate/prospective-students/">Prospective Majors</a></li> <li id="menu-item-7982" class="menu-item menu-item-type-post_type menu-item-object-page menu-item-7982"><a href="https://www.physics.wisc.edu/undergraduate/the-physics-major/">Current students</a></li> <li id="menu-item-7985" class="menu-item menu-item-type-post_type menu-item-object-page menu-item-7985"><a href="https://www.physics.wisc.edu/courses/">Courses</a></li> <li id="menu-item-9664" class="menu-item menu-item-type-post_type menu-item-object-page menu-item-9664"><a href="https://www.physics.wisc.edu/undergraduate/certificate-in-physics/">Certificate in Physics</a></li> <li id="menu-item-7983" class="menu-item menu-item-type-post_type menu-item-object-page menu-item-7983"><a href="https://www.physics.wisc.edu/undergraduate/contact-us/">Advising and Course Enrollment Assistance</a></li> <li id="menu-item-7986" class="menu-item menu-item-type-custom menu-item-object-custom menu-item-7986"><a href="https://www.physics.wisc.edu/undergraduate/files/Physics-Declaration-Form.pdf">Major declaration form</a></li> <li id="menu-item-7987" class="menu-item menu-item-type-custom menu-item-object-custom menu-item-7987"><a href="https://www.physics.wisc.edu/undergraduate/files/Independent-Study-Course-Approval-Form-online.pdf">Independent study approval form</a></li> <li id="menu-item-9862" class="menu-item menu-item-type-custom menu-item-object-custom menu-item-9862"><a href="https://visp.wisc.edu/thematic-physics/">Visiting Scholars (VISP)</a></li> </ul> </li> <li id="menu-item-6319" class="menu-item menu-item-type-post_type menu-item-object-page menu-item-6319"><a href="https://www.physics.wisc.edu/research/">Research</a></li> <li id="menu-item-2923" class="menu-item menu-item-type-post_type menu-item-object-page menu-item-has-children uw-dropdown menu-item-2923"><a href="https://www.physics.wisc.edu/people/" aria-haspopup="true" aria-expanded="false">People<svg class="uw-caret" viewBox="0 0 1792 1792" version="1.1" role="img" focusable="false" aria-hidden="true" aria-labelledby="dynid67501fbee11228.42009868"> <title id="dynid67501fbee11228.42009868">Expand</title> <path d="M1395 736q0 13-10 23l-466 466q-10 10-23 10t-23-10l-466-466q-10-10-10-23t10-23l50-50q10-10 23-10t23 10l393 393 393-393q10-10 23-10t23 10l50 50q10 10 10 23z"/> </svg><svg class="uw-caret" viewBox="0 0 1792 1792" version="1.1" role="img" focusable="false" aria-hidden="true" aria-labelledby="dynid67501fbee11c70.18046468"> <title id="dynid67501fbee11c70.18046468">Collapse</title> <path d="M1395 1184q0 13-10 23l-50 50q-10 10-23 10t-23-10l-393-393-393 393q-10 10-23 10t-23-10l-50-50q-10-10-10-23t10-23l466-466q10-10 23-10t23 10l466 466q10 10 10 23z"/> </svg></a> <ul aria-hidden="true" aria-label="People submenu" class="sub-menu uw-child-menu"> <li id="menu-item-3052" class="menu-item menu-item-type-post_type menu-item-object-page menu-item-3052"><a href="https://www.physics.wisc.edu/people/faculty/">Faculty</a></li> <li id="menu-item-3056" class="menu-item menu-item-type-post_type menu-item-object-page menu-item-3056"><a href="https://www.physics.wisc.edu/people/visitors/">Visiting Faculty and Researchers</a></li> <li id="menu-item-3057" class="menu-item menu-item-type-post_type menu-item-object-page menu-item-3057"><a href="https://www.physics.wisc.edu/people/department/">Department Staff</a></li> <li id="menu-item-3058" class="menu-item menu-item-type-post_type menu-item-object-page menu-item-3058"><a href="https://www.physics.wisc.edu/people/research-staff/">Research Staff</a></li> <li id="menu-item-3059" class="menu-item menu-item-type-post_type menu-item-object-page menu-item-3059"><a href="https://www.physics.wisc.edu/people/phd-students/">PhD Students</a></li> <li id="menu-item-3627" class="menu-item menu-item-type-post_type menu-item-object-page menu-item-3627"><a href="https://www.physics.wisc.edu/people/mspqc-students/">MSPQC Students</a></li> <li id="menu-item-3053" class="menu-item menu-item-type-post_type menu-item-object-page menu-item-3053"><a href="https://www.physics.wisc.edu/people/emeritus-faculty/">Emeritus Faculty</a></li> <li id="menu-item-3061" class="menu-item menu-item-type-post_type menu-item-object-page menu-item-3061"><a href="https://www.physics.wisc.edu/people/board-of-visitors/">Board of Visitors</a></li> <li id="menu-item-12265" class="menu-item menu-item-type-post_type menu-item-object-page menu-item-12265"><a href="https://www.physics.wisc.edu/people/search/">Search for People</a></li> </ul> </li> <li id="menu-item-7957" class="menu-item menu-item-type-custom menu-item-object-custom menu-item-has-children uw-dropdown menu-item-7957"><a href="https://www.physics.wisc.edu/news/" aria-haspopup="true" aria-expanded="false">News &amp; Events<svg class="uw-caret" viewBox="0 0 1792 1792" version="1.1" role="img" focusable="false" aria-hidden="true" aria-labelledby="dynid67501fbee15b62.91414157"> <title id="dynid67501fbee15b62.91414157">Expand</title> <path d="M1395 736q0 13-10 23l-466 466q-10 10-23 10t-23-10l-466-466q-10-10-10-23t10-23l50-50q10-10 23-10t23 10l393 393 393-393q10-10 23-10t23 10l50 50q10 10 10 23z"/> </svg><svg class="uw-caret" viewBox="0 0 1792 1792" version="1.1" role="img" focusable="false" aria-hidden="true" aria-labelledby="dynid67501fbee165b9.81235334"> <title id="dynid67501fbee165b9.81235334">Collapse</title> <path d="M1395 1184q0 13-10 23l-50 50q-10 10-23 10t-23-10l-393-393-393 393q-10 10-23 10t-23-10l-50-50q-10-10-10-23t10-23l466-466q10-10 23-10t23 10l466 466q10 10 10 23z"/> </svg></a> <ul aria-hidden="true" aria-label="News &amp; Events submenu" class="sub-menu uw-child-menu"> <li id="menu-item-7959" class="menu-item menu-item-type-post_type menu-item-object-page menu-item-7959"><a href="https://www.physics.wisc.edu/events/">Events</a></li> <li id="menu-item-7958" class="menu-item menu-item-type-post_type menu-item-object-page menu-item-7958"><a href="https://www.physics.wisc.edu/news/">Department News</a></li> <li id="menu-item-7960" class="menu-item menu-item-type-post_type menu-item-object-page menu-item-7960"><a href="https://www.physics.wisc.edu/department/alumni-friends/">The Wisconsin Physicist</a></li> <li id="menu-item-7961" class="menu-item menu-item-type-custom menu-item-object-custom menu-item-7961"><a href="https://explore.wisc.edu/physics-subscriptions">Subscribe to e-newsletter</a></li> </ul> </li> <li id="menu-item-5126" class="menu-item menu-item-type-post_type menu-item-object-page menu-item-5126"><a href="https://www.physics.wisc.edu/department/climate-diversity/">Climate &amp; Diversity</a></li> <li id="menu-item-6209" class="menu-item menu-item-type-post_type menu-item-object-page menu-item-6209"><a href="https://www.physics.wisc.edu/outreach/">Outreach</a></li> <li id="menu-item-7964" class="menu-item menu-item-type-custom menu-item-object-custom menu-item-home menu-item-has-children uw-dropdown menu-item-7964"><a href="https://www.physics.wisc.edu/" aria-haspopup="true" aria-expanded="false">Resources<svg class="uw-caret" viewBox="0 0 1792 1792" version="1.1" role="img" focusable="false" aria-hidden="true" aria-labelledby="dynid67501fbee19a40.00614801"> <title id="dynid67501fbee19a40.00614801">Expand</title> <path d="M1395 736q0 13-10 23l-466 466q-10 10-23 10t-23-10l-466-466q-10-10-10-23t10-23l50-50q10-10 23-10t23 10l393 393 393-393q10-10 23-10t23 10l50 50q10 10 10 23z"/> </svg><svg class="uw-caret" viewBox="0 0 1792 1792" version="1.1" role="img" focusable="false" aria-hidden="true" aria-labelledby="dynid67501fbee1a4b0.77874010"> <title id="dynid67501fbee1a4b0.77874010">Collapse</title> <path d="M1395 1184q0 13-10 23l-50 50q-10 10-23 10t-23-10l-393-393-393 393q-10 10-23 10t-23-10l-50-50q-10-10-10-23t10-23l466-466q10-10 23-10t23 10l466 466q10 10 10 23z"/> </svg></a> <ul aria-hidden="true" aria-label="Resources submenu" class="sub-menu uw-child-menu"> <li id="menu-item-7965" class="menu-item menu-item-type-post_type menu-item-object-page menu-item-7965"><a href="https://www.physics.wisc.edu/department/">Department Resources</a></li> <li id="menu-item-7990" class="menu-item menu-item-type-post_type menu-item-object-page menu-item-7990"><a href="https://www.physics.wisc.edu/uw-student-resources/">Student Resources</a></li> </ul> </li> <li id="menu-item-7968" class="menu-item menu-item-type-custom menu-item-object-custom menu-item-7968"><a href="https://www.physics.wisc.edu/giving/">Giving</a></li> </ul> </nav> </div> <div class="uw-secondary-nav"> <nav class="uw-nav-menu uw-nav-menu-secondary" aria-label="Secondary Menu"> <ul id="uw-secondary-nav" class="utility-menu"><li id="menu-item-1411" class="menu-item menu-item-type-post_type menu-item-object-page menu-item-1411"><a href="https://www.physics.wisc.edu/department/contact/">Contact</a></li> <li id="menu-item-4302" class="menu-item menu-item-type-post_type menu-item-object-page menu-item-4302"><a href="https://www.physics.wisc.edu/courses/">Courses</a></li> <li id="menu-item-3726" class="menu-item menu-item-type-post_type menu-item-object-page menu-item-3726"><a href="https://www.physics.wisc.edu/department/employment/">Jobs</a></li> <li id="menu-item-7971" class="menu-item menu-item-type-custom menu-item-object-custom menu-item-7971"><a href="https://www.physics.wisc.edu/department/visit/">Visit</a></li> <a href="https://www.physics.wisc.edu/wp-login.php?redirect_to=%2Ftag%2Fentanglement%2F&#038;action=shibboleth">Log in</a></ul> </nav> </div> </div> <nav class="breadcrumb-nav" aria-label="Breadcrumb"> <ol itemscope itemtype="http://schema.org/BreadcrumbList" id="breadcrumbs" class="breadcrumb-nav__list breadcrumbs"> <li itemprop="itemListElement" itemscope itemtype="http://schema.org/ListItem" class="breadcrumb-nav__item item-home"> <a itemprop="item" href="https://www.physics.wisc.edu/" class="breadcrumb-nav__link bread-link bread-home" title="Home" > <span itemprop="name">Home</span> <meta itemprop="position" content="1"> </a> </li> <li itemprop="itemListElement" itemscope itemtype="http://schema.org/ListItem" class="breadcrumb-nav__item item-current item-tag-293 item-tag-entanglement"> <a itemprop="item" href="https://www.physics.wisc.edu/tag/entanglement/" class="breadcrumb-nav__link bread-current bread-tag-293 bread-tag-entanglement" title="Tag: entanglement" aria-current="page"> <span itemprop="name">Tag: entanglement</span> <meta itemprop="position" content="2"> </a> </li> </ol> </nav> <div id="page" class="content"> <main id="main" class="site-main" role="main"> <header class="page-header"> <h1 class="page-title uw-mini-bar">entanglement</h1> </header> <article id="post-11551" class="post-11551 post type-post status-publish format-standard has-post-thumbnail hentry category-astrophysics category-nuclear-physics category-particle-physics category-quantum-science tag-entanglement tag-i-process tag-neutrinos tag-neutron-capture tag-nucleosynthesis tag-standard-model"> <header class="entry-header"> <h1 class="page-title uw-mini-bar">Entangled neutrinos may lead to heavier element formation</h1> <div class="entry-meta"> <span class="posted-on">Posted on <a href="https://www.physics.wisc.edu/2024/06/06/entangled-neutrinos-may-lead-to-heavier-element-formation/" rel="bookmark"><time class="entry-date published updated" datetime="2024-06-06T16:05:27-05:00">June 6, 2024</time></a></span> </div><!-- .entry-meta --> </header> <div class="entry-content"> <p>Elements are the building blocks of every chemical in the universe, but how and where the different elements formed is not entirely understood. A new paper in <a href="https://iopscience.iop.org/article/10.3847/1538-4357/ad393d">The Astrophysical Journal</a> by University of Wisconsin–Madison physics professor <a href="https://www.physics.wisc.edu/directory/balantekin-a-b/">Baha Balantekin</a> and colleagues with the <a href="https://n3as.berkeley.edu/">Network for Neutrinos, Nuclear Astrophysics, and Symmetries</a> (N3AS) Physics Frontier Center, shows how entangled neutrinos could be required for the formation of elements above approximately atomic number 140 via neutron capture in an intermediate-rate process, or i-process.</p> <figure id="attachment_6863" class="wp-caption alignleft" style="max-width: 300px;" aria-label="Baha Balantekin"><a href="https://www.physics.wisc.edu/wp-content/uploads/2022/05/20220506_Banquet_009-scaled-e1652203155678.jpg"><img fetchpriority="high" decoding="async" class="wp-image-6863 size-medium" src="https://www.physics.wisc.edu/wp-content/uploads/2022/05/20220506_Banquet_009-scaled-e1652203155678-300x300.jpg" alt="Profile photo of Baha Balantekin" width="300" height="300" srcset="https://www.physics.wisc.edu/wp-content/uploads/2022/05/20220506_Banquet_009-scaled-e1652203155678-300x300.jpg 300w, https://www.physics.wisc.edu/wp-content/uploads/2022/05/20220506_Banquet_009-scaled-e1652203155678-1024x1024.jpg 1024w, https://www.physics.wisc.edu/wp-content/uploads/2022/05/20220506_Banquet_009-scaled-e1652203155678-150x150.jpg 150w, https://www.physics.wisc.edu/wp-content/uploads/2022/05/20220506_Banquet_009-scaled-e1652203155678-768x768.jpg 768w, https://www.physics.wisc.edu/wp-content/uploads/2022/05/20220506_Banquet_009-scaled-e1652203155678-1200x1200.jpg 1200w, https://www.physics.wisc.edu/wp-content/uploads/2022/05/20220506_Banquet_009-scaled-e1652203155678-400x400.jpg 400w, https://www.physics.wisc.edu/wp-content/uploads/2022/05/20220506_Banquet_009-scaled-e1652203155678.jpg 1401w" sizes="(max-width: 300px) 100vw, 300px" /></a><figcaption class="wp-caption-text">Baha Balantekin</figcaption></figure> <p><em>Why it’s important</em></p> <p>“Where the chemical elements are made is not clear, and we do not know all the possible ways they can be made,” Balantekin says. “We believe that some are made in supernovae explosions or neutron star mergers, and many of these objects are governed by the laws of quantum mechanics, so then you can use the stars to explore aspects of quantum mechanics.”</p> <p><em>What is already known? </em></p> <ul> <li>Immediately after the Big Bang, lighter elements like hydrogen and helium were abundant. Heavier elements, up to iron (atomic number 26) continued to form through nuclear fusion in the centers of hot stars.</li> <li>Above iron, fusion is no longer energetically favorable, and nuclear synthesis occurs via neutron capture, where neutrons glom onto atomic nuclei. At high enough concentrations, neutrons can convert into protons, increasing the atomic number of the element by one.</li> <li>This conversion is dependent on neutrinos and antineutrinos. Neutron capture has been found to occur slowly (s-process, over years) and rapidly (r-process, within minutes); an intermediate timescale, or i-process has been proposed but little evidence exists to support it. Rapid or intermediate neutron capture can only take place in catastrophic events where a huge amount of energy is released, such as supernova collapse.</li> <li>“When a supernova collapse occurs, you start with a big star, which is gravitationally bound, and that binding has energy,” Balantekin says. “When it collapses, that energy has to be released, and it turns out that energy is released in neutrinos.”</li> <li>The laws of quantum mechanics state that those neutrinos can become entangled because they interact in the collapsing supernova. Entanglement is when any two or more particles interacted and then “remember” the others, no matter how far apart they might be.</li> </ul> <p><em>A quick summary of the research</em></p> <ul> <li>“One question we can ask is if these neutrinos are entangled with each other or not,” Balantekin says. “This paper shows that if the neutrinos are entangled, then there is an enhanced new process of element production, the i-process.”</li> </ul> <figure id="attachment_11552" class="wp-caption aligncenter" style="max-width: 640px;" aria-label="The abundance pattern based on calculations in this paper (ν i-process pattern; purple line), compared with the solar system s-process (gray line) and r-process (black line) abundance data (Sneden et al. 2008). The ν i abundance for A = 143 is scaled to the solar r-process data for pattern comparison. | Source: The Astrophysical Journal"><a href="https://www.physics.wisc.edu/wp-content/uploads/2024/06/i-process-APJ-figure-13-entangled-neutrinos.jpeg"><img decoding="async" class="size-large wp-image-11552" src="https://www.physics.wisc.edu/wp-content/uploads/2024/06/i-process-APJ-figure-13-entangled-neutrinos-1024x746.jpeg" alt="a plot of mass number A (atomic number) on the x-axis and abundance as a log scale on the y-axis. a purple line shows the i-process abundance, black line shows r-process, and grey line shows s-process. Above atomic number 140 or so, there is a visible enhancement of the purple line over the other two lines (below 140 the black and grey lines are much higher abundance values than the purple line)" width="640" height="466" srcset="https://www.physics.wisc.edu/wp-content/uploads/2024/06/i-process-APJ-figure-13-entangled-neutrinos-1024x746.jpeg 1024w, https://www.physics.wisc.edu/wp-content/uploads/2024/06/i-process-APJ-figure-13-entangled-neutrinos-300x219.jpeg 300w, https://www.physics.wisc.edu/wp-content/uploads/2024/06/i-process-APJ-figure-13-entangled-neutrinos-768x560.jpeg 768w, https://www.physics.wisc.edu/wp-content/uploads/2024/06/i-process-APJ-figure-13-entangled-neutrinos-1200x874.jpeg 1200w, https://www.physics.wisc.edu/wp-content/uploads/2024/06/i-process-APJ-figure-13-entangled-neutrinos.jpeg 1500w" sizes="(max-width: 640px) 100vw, 640px" /></a><figcaption class="wp-caption-text">The abundance pattern based on calculations in this paper (ν i-process pattern; purple line), compared with the solar system s-process (gray line) and r-process (black line) abundance data (Sneden et al. 2008). The ν i abundance for A = 143 is scaled to the solar r-process data for pattern comparison. | Source: The Astrophysical Journal</figcaption></figure> <p><em>The experimental and simulated evidence</em></p> <ul> <li>The researchers used two known facts to set up their calculations: well-established rates of neutron capture, and catalogs of the atomic spectra of stars, which astronomers have collected over decades to identify the abundance of different elements. They also knew that a supernova collapse produces on the order of 10^58 neutrinos, a number that is far too large to use in any standard calculations.</li> <li>Instead, they made simulations of up to eight neutrinos and calculated the abundance of elements that would be created via neutron capture if the neutrinos were entangled, or were not entangled.</li> <li>“We have a system of, say, three neutrinos and three antineutrinos together in a region where there are protons and neutrons and see if that changes anything about element formation,” Balantekin says. “We calculate the abundances of elements that are produced in the star, and you see that the entangled or not entangled cases give you different abundances.”</li> <li>The simulations showed that elements with atomic number greater than 140 are likely to be enhanced by i-process neutron capture — but only if the neutrinos are entangled.</li> </ul> <p><em>Caveats and future work</em></p> <ul> <li>Balantekin points out that these simulations are just “hints” based on astronomical observations. Astrophysics research requires using the cosmos as a lab, and it is difficult to conduct true experimental tests on earth.</li> <li>“There’s something called the standard model of particle physics, which determines the interaction of particles. The neutrino-neutrino interaction is one aspect of the standard model which has not been tested in the lab, it can only be tested in astrophysical extremes,” Balantekin says. “But other aspects of the standard model have been tested in the lab, so one believes that it should all work.”</li> <li>The researchers are currently using more astrophysical data of element abundance in extreme environments to see if those abundances continue to be explained by entangled neutrinos.</li> </ul> <p><em>This research is supported in part by the National Science Foundation grants Nos. PHY-1630782 and PHY-2020275 (Network for Neutrinos, Nuclear Astrophysics and Symmetries). Balantekin is supported in part by the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award No. DE-SC0019465 and in part by the National Science Foundation Grant PHY-2108339 at the University of Wisconsin-Madison. </em></p> <p><em>The paper&#8217;s co-authors include Michael Cervia, Amol Patwardhan, Rebecca Surman, and Xilu Wang, all current or former members of N3AS.</em></p> </div> <footer class="entry-footer"> <span class="cat-links">Posted in <a href="https://www.physics.wisc.edu/category/astrophysics/" rel="category tag">Astrophysics</a>, <a href="https://www.physics.wisc.edu/category/nuclear-physics/" rel="category tag">nuclear physics</a>, <a href="https://www.physics.wisc.edu/category/particle-physics/" rel="category tag">particle physics</a>, <a href="https://www.physics.wisc.edu/category/quantum-science/" rel="category tag">Quantum Science</a></span><span class="tags-links">Tagged <a href="https://www.physics.wisc.edu/tag/entanglement/" rel="tag">entanglement</a>, <a href="https://www.physics.wisc.edu/tag/i-process/" rel="tag">i process</a>, <a href="https://www.physics.wisc.edu/tag/neutrinos/" rel="tag">neutrinos</a>, <a href="https://www.physics.wisc.edu/tag/neutron-capture/" rel="tag">neutron capture</a>, <a href="https://www.physics.wisc.edu/tag/nucleosynthesis/" rel="tag">nucleosynthesis</a>, <a href="https://www.physics.wisc.edu/tag/standard-model/" rel="tag">standard model</a></span> </footer> </article> <article id="post-11489" class="post-11489 post type-post status-publish format-standard has-post-thumbnail hentry category-awards-and-honors category-graduate-students category-mspqc category-quantum-computing tag-computer-sciences tag-entanglement tag-mspqc tag-qed-c tag-quantum-computing tag-quantum-science tag-qubits tag-student-research tag-wqi"> <header class="entry-header"> <h1 class="page-title uw-mini-bar">MSPQC&#8217;s Preetham Tikkireddi wins second place at QED-C student poster presentation</h1> <div class="entry-meta"> <span class="posted-on">Posted on <a href="https://www.physics.wisc.edu/2024/05/23/preetham-tikkireddi-qed-c/" rel="bookmark"><time class="entry-date published updated" datetime="2024-05-23T16:30:03-05:00">May 23, 2024</time></a></span> </div><!-- .entry-meta --> </header> <div class="entry-content"> <p><a href="https://www.physics.wisc.edu/graduate/mspqc-program/">MSPQC</a> student Preetham Tikkireddi won second place for his poster, “Understanding security side channel attacks on multi-tenancy quantum computers,” at the <a href="https://quantumconsortium.org/blog/highlights-from-the-qed-c-plenary-meeting-in-evanston/">plenary meeting</a> of the Quantum Economic Development Consortium (QED-C), held March 20-21 in Evanston, IL.</p> <p>Students who attended the plenary first learned best practices for presenting their research to a non-science audience, a useful skill for a cutting-edge field where investors, hiring managers, and policy makers do not necessarily have a quantum background. Then, the students implemented those skills at the judged poster session.</p> <p>“[The poster session attendees] are really smart people, but they&#8217;re not quantum people, so you set them up for asking questions, and based on the questions that they&#8217;re asking, you determine how deep you want to go into your research.” Tikkireddi says. “It was a very different kind of experience, rather than just a plain research presentation to a professor or people who already know the field.”</p> <figure id="attachment_11490" class="wp-caption aligncenter" style="max-width: 640px;" aria-label="A total of 17 students presented posters at the first-ever QED-C student program and poster competition. UW–Madison MSPQC student Preetham Tikkireddi (right) was one of three graduate students to win the top honor at the competition. | Photo credit: QED-C"><a href="https://www.physics.wisc.edu/wp-content/uploads/2024/05/Preetham-QED-C-winners.jpeg"><img decoding="async" class="size-large wp-image-11490" src="https://www.physics.wisc.edu/wp-content/uploads/2024/05/Preetham-QED-C-winners-1024x555.jpeg" alt="a group of people in business attire stand and pose in a line, they all have nametag lanyards around their necks" width="640" height="347" srcset="https://www.physics.wisc.edu/wp-content/uploads/2024/05/Preetham-QED-C-winners-1024x555.jpeg 1024w, https://www.physics.wisc.edu/wp-content/uploads/2024/05/Preetham-QED-C-winners-300x163.jpeg 300w, https://www.physics.wisc.edu/wp-content/uploads/2024/05/Preetham-QED-C-winners-768x416.jpeg 768w, https://www.physics.wisc.edu/wp-content/uploads/2024/05/Preetham-QED-C-winners.jpeg 1200w" sizes="(max-width: 640px) 100vw, 640px" /></a><figcaption class="wp-caption-text">A total of 17 students presented posters at the first-ever QED-C student program and poster competition. UW–Madison MSPQC student Preetham Tikkireddi (right) was one of three graduate students to win the top honor at the competition. | Photo credit: QED-C</figcaption></figure> <p>Tikkireddi’s research, conducted with computer sciences professor <a href="https://quest-lab.cs.wisc.edu/">Swamit Tannu</a>, looked at the potential for exploiting crosstalk when two users access the same quantum computer at the same time.</p> <p>“Right now, quantum computers are really expensive, and the way we access them is by sending jobs to these quantum providers like IBM or IonQ,” Tikkireddi explains. “But the queues are really long. If you&#8217;re lucky, you can get the results back the next day.”</p> <p>Quantum computing capacity is growing rapidly in the form of more and more qubits, and most jobs submitted to these long queues do not need to use all the qubits. Tikkireddi and Tannu thought that one way to increase throughput would be to allow users to share the same quantum computer, each using a subset of the qubits. But quantum computations rely on qubit entanglement, where physically separate qubits interact and share information. It was unclear if sharing a quantum computer opens users to security risks.</p> <p>In his work, Tikkireddi asked if he could count C-NOTs — the gate that is used to create this entanglement — of another user. He entangled two qubits, then asked if two other qubits could “hear” what the first two were doing.</p> <p>“We were able to use that to figure out how many C-NOTs the other guy is doing. That’s step one of an attack,” Tikkireddi says. “Your algorithm is your intellectual property, so you don&#8217;t want people to steal it. It’s a security problem.”</p> <p>With this initial analysis identifying potential security risks amongst shared quantum computer use, Tikkireddi says providers should currently not let users share computing time, and that future research should focus on ways to mitigate these crosstalk attacks in an effort to balance efficiency with safeguarding intellectual property.</p> <p>Tikkireddi credits Tannu for helping to guide his poster away from a traditional research poster and toward one more accessible to a non-science audience. He also appreciates the support from MSQPC associate director Katerina Moloni for encouraging and preparing students to take advantage of these training opportunities.</p> <p>“It was a really good networking opportunity, especially for me, who is looking for a job right now,” Tikkireddi says. “I would highly recommend students to go to these kinds of events because we get a chance to interact with people in the industry.”</p> </div> <footer class="entry-footer"> <span class="cat-links">Posted in <a href="https://www.physics.wisc.edu/category/awards-and-honors/" rel="category tag">Awards and Honors</a>, <a href="https://www.physics.wisc.edu/category/graduate-students/" rel="category tag">Graduate Students</a>, <a href="https://www.physics.wisc.edu/category/mspqc/" rel="category tag">MSPQC</a>, <a href="https://www.physics.wisc.edu/category/quantum-computing/" rel="category tag">Quantum Computing</a></span><span class="tags-links">Tagged <a href="https://www.physics.wisc.edu/tag/computer-sciences/" rel="tag">computer sciences</a>, <a href="https://www.physics.wisc.edu/tag/entanglement/" rel="tag">entanglement</a>, <a href="https://www.physics.wisc.edu/tag/mspqc/" rel="tag">MSPQC</a>, <a href="https://www.physics.wisc.edu/tag/qed-c/" rel="tag">QED-C</a>, <a href="https://www.physics.wisc.edu/tag/quantum-computing/" rel="tag">quantum computing</a>, <a href="https://www.physics.wisc.edu/tag/quantum-science/" rel="tag">quantum science</a>, <a href="https://www.physics.wisc.edu/tag/qubits/" rel="tag">qubits</a>, <a href="https://www.physics.wisc.edu/tag/student-research/" rel="tag">student research</a>, <a href="https://www.physics.wisc.edu/tag/wqi/" rel="tag">WQI</a></span> </footer> </article> </main> </div> <footer id="colophon" class="uw-footer"> <h2 class="show-for-sr uw-footer-header">Site footer content</h2> <div class="uw-footer-content"> <div class="uw-logo"> <div class="uw-logo-link-wrapper"><a href="https://www.wisc.edu" aria-label="Link to main university website"> <svg viewBox="0 0 326 216" version="1.1" role="img" focusable="false" aria-labelledby="dynid67501fbee7efa1.20190057"> <title id="dynid67501fbee7efa1.20190057">University logo that links to main university website</title> <g> <path d="M21.3,195.1c-5.7-4.1-6.2-3.7-8.3-10.1l-7.3-23c-1.1-3.4-2.1-7.5-5.2-9.6v-0.2h9.1c-0.2,1.4,0.4,3.3,0.7,4.5l9.3,28.9 l7.3-23.7c1.2-3.8,2.4-7.8-1-9.6v-0.2h8.8c-0.4,1.6,0.1,3.5,0.9,6.3l8.7,27l7-22.8c1.1-3.5,3.2-8.6-1.7-10.3v-0.2h9.6l-13.1,42.8 c-5.7-3.9-6.2-3.6-8.2-10L31,163.7L21.3,195.1z"/> <path d="M64.5,161.1c0-2.9,0.4-7.4-2.7-8.6v-0.2h11.8v0.2c-3.1,1.2-2.7,5.8-2.7,8.6v23.5c0,2.8-0.4,7.3,2.7,8.5v0.2H61.7v-0.2 c3.1-1.1,2.7-5.7,2.7-8.5V161.1z"/> <path d="M102.2,159.7c-2.4-2.5-6.3-3.9-9.8-3.9c-3.5,0-8,1.4-8,5.7c0,8.5,21.4,8.4,21.4,19.9c0,6.7-7,12.9-16.7,12.9 c-3.8,0-7.6-0.6-11.1-1.9l-1.8-7.8c3.7,3.2,8.8,5.2,13.6,5.2c3.5,0,8.9-2.1,8.9-6.5c0-9.7-21.4-8-21.4-21.2c0-7.8,8-10.8,15.6-10.8 c3.1,0,6.3,0.4,9.3,1.4V159.7z"/> <path d="M141.5,160c-3.4-2.2-7.4-3.5-11.5-3.5c-8.6,0-14.6,6.3-14.6,15.3c0,9.2,6.2,17.3,15.8,17.3c4.7,0,9.3-1.7,13.3-3.9h0.2 l-3.2,7.2c-2.9,1.4-6.2,1.9-9.4,1.9c-14.7,0-23.8-8.2-23.8-21.5c0-12.9,9.1-21.4,21.8-21.4c3.8,0,7.7,0.7,11.3,1.6V160z"/> <path d="M189.9,172.3c0,12.7-10.5,21.9-22.9,21.9c-12.3,0-22.7-8.8-22.7-21.6c0-11.8,10.3-21.7,23.3-21.4 C180.7,151.2,189.9,161.1,189.9,172.3z M151.3,172.1c0,8.7,6.2,17.7,15.9,17.7c9.5,0,15.5-6.9,15.5-16.2c0-9.1-5.8-17.9-15.6-17.9 C157.5,155.7,151.3,162.7,151.3,172.1z"/> <path d="M199.3,185.2c0,3.5-0.1,6,3.2,7.9v0.2h-11v-0.2c3.3-1.9,3.3-4.4,3.3-7.9v-24.8c0-3.5,0-6-3.2-7.8v-0.2h9.1v0.1 c0.2,0.7,0.5,1.1,0.9,1.6l0.9,1.2l22.8,28.8v-23.6c0-3.5,0.1-6-3.2-7.8v-0.2h11v0.2c-3.2,1.9-3.2,4.4-3.2,7.8v34.9 c-4.4-1.5-6.4-3.5-9.1-7.1l-21.4-27.1V185.2z"/> <path d="M261.2,159.7c-2.4-2.5-6.3-3.9-9.8-3.9c-3.5,0-8,1.4-8,5.7c0,8.5,21.4,8.4,21.4,19.9c0,6.7-7,12.9-16.7,12.9 c-3.8,0-7.6-0.6-11.1-1.9l-1.8-7.8c3.7,3.2,8.8,5.2,13.6,5.2c3.5,0,8.9-2.1,8.9-6.5c0-9.7-21.4-8-21.4-21.2c0-7.8,8-10.8,15.6-10.8 c3.1,0,6.3,0.4,9.3,1.4V159.7z"/> <path d="M270.7,161.1c0-2.9,0.4-7.4-2.7-8.6v-0.2h11.8v0.2c-3.1,1.2-2.7,5.8-2.7,8.6v23.5c0,2.8-0.4,7.3,2.7,8.5v0.2H268v-0.2 c3.1-1.1,2.7-5.7,2.7-8.5V161.1z"/> <path d="M291.8,185.2c0,3.5-0.1,6,3.2,7.9v0.2h-11v-0.2c3.3-1.9,3.3-4.4,3.3-7.9v-24.8c0-3.5,0-6-3.2-7.8v-0.2h9.1v0.1 c0.2,0.7,0.5,1.1,0.9,1.6l0.9,1.2l22.8,28.8v-23.6c0-3.5,0.1-6-3.2-7.8v-0.2h11v0.2c-3.2,1.9-3.2,4.4-3.2,7.8v34.9 c-4.4-1.5-6.4-3.5-9.1-7.1l-21.4-27.1V185.2z"/> </g> <g> <path d="M11.7,203.2v7c0,2.7,1.5,3.5,3,3.5c1.7,0,3-0.8,3-3.5v-7h1.5v6.9c0,3.8-2.1,4.8-4.5,4.8c-2.4,0-4.5-1.2-4.5-4.7v-7H11.7z"/> <path d="M22.3,214.8v-11.6h2c1.7,2.7,5.3,8.5,5.9,9.7h0c-0.1-1.5-0.1-3.3-0.1-5.2v-4.5h1.4v11.6h-1.9c-1.5-2.5-5.3-8.7-6-10h0 c0.1,1.3,0.1,3.3,0.1,5.4v4.6H22.3z"/> <path d="M36.6,203.2v11.6h-1.5v-11.6H36.6z"/> <path d="M42.9,214.8l-4.2-11.6h1.6l2,5.8c0.6,1.7,1.2,3.4,1.4,4.5h0c0.2-0.9,0.9-2.7,1.5-4.4l2.1-5.8H49l-4.4,11.6H42.9z"/> <path d="M58.4,209.3h-5.7v4.1H59l-0.2,1.3h-7.6v-11.6h7.5v1.3h-6v3.5h5.7V209.3z"/> <path d="M63,209.7v5.1h-1.5v-11.6H66c2.4,0,3.6,1.3,3.6,3.1c0,1.5-0.9,2.4-2,2.7c0.9,0.2,1.8,1,1.8,3v0.5c0,0.8,0,1.8,0.2,2.3h-1.5 c-0.2-0.5-0.2-1.4-0.2-2.5V212c0-1.6-0.5-2.4-2.5-2.4H63z M63,208.4h2.5c1.8,0,2.5-0.7,2.5-2c0-1.2-0.8-1.9-2.4-1.9H63V208.4z"/> <path d="M73.3,211.5c0.3,1.4,1.3,2.1,2.9,2.1c1.8,0,2.5-0.8,2.5-1.9c0-1.2-0.6-1.8-2.9-2.4c-2.7-0.7-3.7-1.6-3.7-3.2 c0-1.7,1.3-3.1,3.8-3.1c2.8,0,3.9,1.6,4.1,3.1h-1.6c-0.2-1-0.8-1.9-2.5-1.9c-1.4,0-2.2,0.6-2.2,1.7c0,1.1,0.6,1.5,2.7,2 c3.3,0.8,3.9,2.1,3.9,3.6c0,1.9-1.4,3.3-4.2,3.3c-2.9,0-4.2-1.6-4.4-3.4H73.3z"/> <path d="M84.5,203.2v11.6H83v-11.6H84.5z"/> <path d="M90.4,204.5h-3.7v-1.3h9v1.3h-3.7v10.3h-1.5V204.5z"/> <path d="M101.2,214.8v-4.2c0-0.1,0-0.2-0.1-0.3l-4.1-7h1.8c1,1.9,2.7,4.9,3.3,5.9c0.5-1,2.2-4,3.3-5.9h1.6l-4.2,7 c0,0.1-0.1,0.1-0.1,0.3v4.2H101.2z"/> <path d="M123.5,208.9c0,3.2-1.8,6-5.4,6c-3.4,0-5.3-2.6-5.3-5.9c0-3.3,1.9-5.9,5.4-5.9C121.5,203,123.5,205.5,123.5,208.9z M114.4,208.9c0,2.5,1.3,4.7,3.8,4.7c2.7,0,3.8-2.2,3.8-4.7c0-2.5-1.2-4.6-3.8-4.6C115.5,204.3,114.4,206.5,114.4,208.9z"/> <path d="M126.3,203.2h7.4v1.3h-5.9v3.8h5.5v1.3h-5.5v5.2h-1.5V203.2z"/> <path d="M142.5,214.8l-3.1-11.6h1.6c0.9,3.8,2.1,8.6,2.4,9.9h0c0.3-1.5,1.9-6.9,2.6-9.9h1.5c0.7,2.6,2.3,8.5,2.5,9.8h0 c0.4-2,2-7.5,2.6-9.8h1.5l-3.4,11.6h-1.6c-0.7-2.7-2.2-8.2-2.5-9.6h0c-0.3,1.7-1.8,6.9-2.6,9.6H142.5z"/> <path d="M158,203.2v11.6h-1.5v-11.6H158z"/> <path d="M162.2,211.5c0.3,1.4,1.3,2.1,2.9,2.1c1.8,0,2.5-0.8,2.5-1.9c0-1.2-0.6-1.8-2.9-2.4c-2.7-0.7-3.7-1.6-3.7-3.2 c0-1.7,1.3-3.1,3.8-3.1c2.8,0,3.9,1.6,4.1,3.1h-1.6c-0.2-1-0.8-1.9-2.5-1.9c-1.4,0-2.2,0.6-2.2,1.7c0,1.1,0.6,1.5,2.7,2 c3.3,0.8,3.9,2.1,3.9,3.6c0,1.9-1.4,3.3-4.2,3.3c-2.9,0-4.2-1.6-4.4-3.4H162.2z"/> <path d="M181.1,211.5c-0.5,2-2,3.4-4.6,3.4c-3.5,0-5.2-2.6-5.2-5.9c0-3.1,1.7-6,5.3-6c2.7,0,4.2,1.6,4.6,3.5h-1.5 c-0.4-1.3-1.2-2.2-3.1-2.2c-2.6,0-3.6,2.3-3.6,4.7c0,2.3,1,4.7,3.7,4.7c1.8,0,2.6-1,3-2.1H181.1z"/> <path d="M193.9,208.9c0,3.2-1.8,6-5.4,6c-3.4,0-5.3-2.6-5.3-5.9c0-3.3,1.9-5.9,5.4-5.9C191.8,203,193.9,205.5,193.9,208.9z M184.7,208.9c0,2.5,1.3,4.7,3.8,4.7c2.7,0,3.8-2.2,3.8-4.7c0-2.5-1.2-4.6-3.8-4.6C185.9,204.3,184.7,206.5,184.7,208.9z"/> <path d="M196.6,214.8v-11.6h2c1.7,2.7,5.3,8.5,5.9,9.7h0c-0.1-1.5-0.1-3.3-0.1-5.2v-4.5h1.4v11.6H204c-1.5-2.5-5.3-8.7-6-10h0 c0.1,1.3,0.1,3.3,0.1,5.4v4.6H196.6z"/> <path d="M210.1,211.5c0.3,1.4,1.3,2.1,2.9,2.1c1.8,0,2.5-0.8,2.5-1.9c0-1.2-0.6-1.8-2.9-2.4c-2.7-0.7-3.7-1.6-3.7-3.2 c0-1.7,1.3-3.1,3.8-3.1c2.8,0,3.9,1.6,4.1,3.1h-1.6c-0.2-1-0.8-1.9-2.5-1.9c-1.4,0-2.2,0.6-2.2,1.7c0,1.1,0.6,1.5,2.7,2 c3.3,0.8,3.9,2.1,3.9,3.6c0,1.9-1.4,3.3-4.2,3.3c-2.9,0-4.2-1.6-4.4-3.4H210.1z"/> <path d="M221.3,203.2v11.6h-1.5v-11.6H221.3z"/> <path d="M224.8,214.8v-11.6h2c1.7,2.7,5.3,8.5,5.9,9.7h0c-0.1-1.5-0.1-3.3-0.1-5.2v-4.5h1.4v11.6h-1.9c-1.5-2.5-5.3-8.7-6-10h0 c0.1,1.3,0.1,3.3,0.1,5.4v4.6H224.8z"/> <path d="M243.4,209.8v1.3h-6.6v-1.3H243.4z"/> <path d="M256.1,209.8c0-2.2,0-4.3,0.1-5.6h-0.1c-0.5,1.9-2.4,6.8-3.7,10.5H251c-1-3-2.9-8.5-3.5-10.5h0c0.1,1.3,0.1,3.9,0.1,5.9 v4.6h-1.4v-11.6h2.3c1.3,3.6,2.9,8.2,3.3,9.7h0c0.3-1.1,2.2-6.2,3.5-9.7h2.2v11.6h-1.5V209.8z"/> <path d="M262.6,211.3l-1.2,3.5h-1.5l4.1-11.6h1.9l4.3,11.6h-1.6l-1.3-3.5H262.6z M266.8,210c-1.1-3-1.7-4.7-2-5.5h0 c-0.3,1-1,2.9-1.8,5.5H266.8z"/> <path d="M272.3,203.2h4.1c3.3,0,5.5,2.2,5.5,5.7c0,3.4-2.1,5.9-5.5,5.9h-4.1V203.2z M273.8,213.5h2.4c2.7,0,4-2,4-4.6 c0-2.3-1.2-4.4-4-4.4h-2.4V213.5z"/> <path d="M286.2,203.2v11.6h-1.5v-11.6H286.2z"/> <path d="M290.3,211.5c0.3,1.4,1.3,2.1,2.9,2.1c1.8,0,2.5-0.8,2.5-1.9c0-1.2-0.6-1.8-2.9-2.4c-2.7-0.7-3.7-1.6-3.7-3.2 c0-1.7,1.3-3.1,3.8-3.1c2.8,0,3.9,1.6,4.1,3.1h-1.6c-0.2-1-0.8-1.9-2.5-1.9c-1.4,0-2.2,0.6-2.2,1.7c0,1.1,0.6,1.5,2.7,2 c3.3,0.8,3.9,2.1,3.9,3.6c0,1.9-1.4,3.3-4.2,3.3c-2.9,0-4.2-1.6-4.4-3.4H290.3z"/> <path d="M310.1,208.9c0,3.2-1.8,6-5.4,6c-3.4,0-5.3-2.6-5.3-5.9c0-3.3,1.9-5.9,5.4-5.9C308.1,203,310.1,205.5,310.1,208.9z M301,208.9c0,2.5,1.3,4.7,3.8,4.7c2.7,0,3.8-2.2,3.8-4.7c0-2.5-1.2-4.6-3.8-4.6C302.2,204.3,301,206.5,301,208.9z"/> <path d="M312.9,214.8v-11.6h2c1.7,2.7,5.3,8.5,5.9,9.7h0c-0.1-1.5-0.1-3.3-0.1-5.2v-4.5h1.4v11.6h-1.9c-1.5-2.5-5.3-8.7-6-10h0 c0.1,1.3,0.1,3.3,0.1,5.4v4.6H312.9z"/> </g> <path d="M211.4,52c-0.3-3-0.8-6-1.4-8.9c-0.6-2.7-1.3-5.4-2.3-8c-1-2.8-2.2-5.5-3.6-8c-1.4-2.4-3-4.6-4.8-6.7 c-4.9-5.4-11.1-8.4-17.8-8.5l-0.1,0c-1.1-2.4-4.1-4.4-6.8-4.7c0,0-1.4-6-7.8-6.1c-6.4,0-7.8,6.1-7.8,6.1c-2.6,0.4-5.7,2.3-6.8,4.7 l-0.1,0c-6.8,0.1-12.9,3.1-17.8,8.5c-1.9,2-3.4,4.3-4.8,6.7c-1.4,2.5-2.6,5.3-3.6,8c-0.9,2.6-1.7,5.3-2.3,8 c-0.6,2.9-1.1,5.9-1.4,8.9c-3.7,36.8,12.8,82,42.5,88.9c0.5,0.7,1.5,2.1,2.1,2.1c0.6,0,1.6-1.4,2.1-2.1 C198.6,134,215.1,88.8,211.4,52z M166.8,2.5c5.2,0,6.4,4.4,6.4,4.5c-2.6,0.2-5,1.7-6.3,4c0,0-0.1,0.2-0.1,0.2 c-0.1,0-0.1-0.1-0.1-0.2c-1.3-2.3-3.7-3.8-6.3-4C160.4,6.9,161.5,2.5,166.8,2.5z M163.7,9.5c1.3,0.8,2.2,2,2.6,3.4 c0.1,0.4,0.3,0.7,0.4,0.7s0.3-0.3,0.4-0.7c0.4-1.4,1.3-2.7,2.6-3.4c3.8-2.3,8.1-0.8,9.8,2.6c-0.9,0.1-1.7,0.4-2.7,0.7 c-1.5,0.5-2.8,1.2-3.9,2.1c-2.4,2.2-4.5,5.6-4.9,9.9c-1.1,11.9,12.6,10,13.2,10c1.8,0,3.1-2.8,3.1-6.5c0-3.7-1.4-6.5-3.1-6.5 c-1.1,0-2.9,0.8-3.1,4.1c-0.1,2.3,1,5.4,2.5,5.6c0.8,0.1,1.5-1.2,1.7-2.6c0.2-1.2,0.1-3-1-3.3c-0.3-0.1-0.7,0.1-0.8,0.5 c-0.1,0.3,0.7,0.8,0.6,2.2c0,2-2.1,1-1.8-2.2c0.2-2.9,1.7-2.7,1.8-2.7c0.8,0,2.1,1.7,2.1,4.9c0,2.8-1.4,5.9-4,4.3 c-2.2-1.6-3.1-5.3-2.5-8.2c0.3-1.3,1.4-4.9,5.1-4.9c5.3,0,10.2,2.8,14.2,8c-0.4,1.4-3.2,6.7-11.8,11.7c-0.2,0.1-0.5,0.3-0.5,0.2 c-2.6-1.1-5.1-1.8-8-1.6c-2.6,0.1-5.1,0.6-7.5,1.2c-0.5,0.1-1,0.2-1.5,0.2c-0.5,0-1-0.1-1.5-0.2c-2.5-0.6-5-1.1-7.5-1.2 c-2.9-0.2-5.4,0.5-8,1.6c0,0-0.3-0.2-0.5-0.2c-8.7-5.1-11.4-10.3-11.8-11.7c3.9-5.2,8.9-8,14.2-8c3.7,0,4.8,3.6,5.1,4.9 c0.6,2.9-0.3,6.6-2.5,8.2c-2.6,1.6-4-1.5-4-4.3c0-3.2,1.2-4.9,2.1-4.9c0.1,0,1.5-0.2,1.8,2.7c0.3,3.2-1.8,4.2-1.8,2.2 c0-1.4,0.7-1.9,0.6-2.2c-0.1-0.3-0.4-0.5-0.8-0.5c-1.1,0.3-1.2,2.1-1,3.3c0.2,1.4,0.9,2.7,1.7,2.6c1.5-0.2,2.6-3.3,2.5-5.6 c-0.2-3.3-2-4.1-3.1-4.1c-1.7,0-3.1,2.8-3.1,6.5c0,3.7,1.3,6.5,3.1,6.5c0.7,0.1,14.3,1.9,13.2-10c-0.4-4.3-2.5-7.7-4.9-9.9 c-1.1-1-2.3-1.6-3.9-2.1c-1.1-0.3-1.8-0.5-2.7-0.7C155.6,8.7,159.9,7.1,163.7,9.5z M138.1,58.5c-4.4-0.4-7.8-1.9-9.4-2.7 c0.7-11.9,3.7-21.2,8.1-27.4c0.8,2,4.2,7.1,12,11.7C142.1,44,139.1,52.3,138.1,58.5z M149.6,41.4c2-1.2,4.5-1.8,7.1-2 c4.5-0.3,7.8,1.4,10,1.5h0.1c2.2-0.1,5.5-1.8,10-1.5c2.6,0.2,5.2,0.7,7.1,2c9.1,5.8,10.4,19.1,10.5,23.5c0.6,15.5-4.2,27.5-5.8,30.9 c-6.3,13.8-13.9,23.6-21.4,26.9l-0.6,0.3l-0.6-0.3c-7.5-3.3-15.1-13.1-21.4-26.9c-1.5-3.3-6.4-15.4-5.8-30.9 C139.2,60.6,140.5,47.2,149.6,41.4z M137.9,59.3c-0.3,2.3-0.5,4.2-0.5,5.4c-0.2,4.3,0,8.6,0.6,12.9c0.6,4,1.5,8,2.7,11.9 c1.7,5.3,4,10.3,6.7,15.2c-2.8,2.5-7,3.5-8.4,3.8c-7.5-15-11.4-34.3-10.5-51.7C130.4,57.6,133.7,59,137.9,59.3z M147.9,105.4 c5,8.6,10,13.8,13.7,16.5c-1.4,3.5-4.6,6.2-5.8,7.1c-6.5-4.4-12-11.3-16.4-19.7C141.2,108.9,145.1,107.9,147.9,105.4z M162.4,122.4 c2,1.5,4.1,2.3,4.3,2.4c0.3-0.1,2.3-0.9,4.3-2.4c1.4,3.4,4.4,6,5.7,7.1c-1.9,1.2-3.8,2.2-5.8,2.9c0-0.1,0-0.1,0-0.2 c-0.4-2.1-3.2-2.6-4.2-2.6c-1,0-3.8,0.4-4.2,2.6c0,0.1,0,0.1,0,0.2c-2-0.7-4-1.7-5.8-2.9C158,128.4,161,125.8,162.4,122.4z M171.9,121.9c3.8-2.7,8.7-7.9,13.7-16.5c2.8,2.5,6.7,3.5,8.4,3.8c-4.3,8.4-9.9,15.3-16.4,19.7C176.5,128.1,173.2,125.4,171.9,121.9 z M186,104.6c2.7-4.8,5-9.9,6.7-15.2c1.2-3.9,2.1-7.9,2.7-11.9c0.6-4.3,0.8-8.6,0.6-12.9c0-1.2-0.2-3.1-0.5-5.4 c4.3-0.4,7.6-1.7,9.3-2.6c0.9,17.4-3,36.8-10.5,51.7C193,108.2,188.8,107.2,186,104.6z M195.4,58.5c-1-6.2-4.1-14.3-10.7-18.5 c7.8-4.6,11.2-9.7,12-11.7c4.4,6.2,7.4,15.5,8.1,27.4C203.3,56.6,199.9,58.1,195.4,58.5z M161.9,138.3c-3.4-1.1-6.6-2.7-9.5-4.8 c-1.9-1.3-3.6-2.7-5.3-4.3c-1.3-1.3-2.6-2.6-3.8-4c-0.8-1-1.6-1.9-2.4-2.9c-3.6-4.8-6.7-10.2-9.1-15.7c-2.3-5.4-4.2-10.9-5.6-16.6 c-1.4-5.8-2.4-11.7-2.9-17.6c-0.5-5.8-0.6-11.8-0.1-17.6c0.3-3.1,0.6-6.3,1.2-9.4c0.6-3.1,1.3-6.1,2.3-9.1c0.9-2.7,2-5.4,3.4-7.9 c1.4-2.6,3.1-5.1,5.1-7.2c1.9-2,4-3.7,6.4-5c1-0.5,2.1-1,3.1-1.4c0.5-0.2,1.1-0.4,1.7-0.5c0.5-0.1,1.1-0.4,1.7-0.4 c1.4-0.3,2.8-0.4,4.2-0.4c1.1,0,3.9,0.2,6.3,1.7c2.7,1.9,5,5,5.4,9.8c0.6,7.3-6.8,8.5-8.3,8.5c-0.2,0-0.3-0.2,0.4-1 c1.7-2.2,2.3-5.6,1.7-8.3c-0.7-3.4-3.1-6-6.5-6c-5.2,0-9.8,2.6-13.2,6.3c-3.3,3.6-5.6,8.2-7.3,12.8c-2.1,5.9-3.2,12.2-3.6,18.5 c-0.4,5.8-0.2,11.6,0.4,17.3c0.6,5.8,1.7,11.6,3.2,17.2c1.5,5.5,3.4,10.9,5.7,16c2.4,5.2,5.3,10.2,8.9,14.7 c3.6,4.5,8.1,8.5,13.2,11.2c1.2,0.6,2.4,1.1,3.6,1.6c-0.1,1.9,0.4,3.6,1.1,5C162.6,138.6,162.6,138.5,161.9,138.3z M167.3,140.8 c0,0-0.3,0.3-0.5,0.3c-0.3,0-0.5-0.3-0.5-0.3c-1.3-1.6-3.2-4.7-2.5-8.4c0.2-1,2-1.5,3-1.5c1,0,2.8,0.5,3,1.5 C170.4,136.1,168.5,139.2,167.3,140.8z M210.2,72.4c-0.5,5.9-1.5,11.8-2.9,17.6c-1.4,5.7-3.2,11.2-5.6,16.6 c-2.4,5.5-5.4,10.9-9.1,15.7c-0.8,1-1.5,2-2.4,2.9c-1.2,1.4-2.5,2.7-3.8,4c-1.6,1.5-3.4,3-5.3,4.3c-2.9,2-6.2,3.7-9.5,4.8 c-0.7,0.2-0.7,0.3-1.5,0.4c0.7-1.4,1.2-3.1,1.1-5c1.2-0.4,2.4-1,3.6-1.6c5.2-2.6,9.6-6.7,13.2-11.2c3.6-4.5,6.5-9.5,8.9-14.7 c2.4-5.2,4.3-10.5,5.7-16c1.5-5.6,2.6-11.4,3.2-17.2c0.6-5.7,0.8-11.5,0.4-17.3c-0.4-6.3-1.5-12.6-3.6-18.5 c-1.6-4.6-3.9-9.2-7.3-12.8c-3.4-3.7-8-6.3-13.2-6.3c-3.4,0-5.8,2.6-6.5,6c-0.6,2.7,0,6.1,1.7,8.3c0.7,0.8,0.6,1,0.4,1 c-1.5,0-9-1.1-8.3-8.5c0.4-4.8,2.8-7.9,5.4-9.8c2.4-1.5,5.2-1.7,6.3-1.7c1.4,0,2.8,0.1,4.2,0.4c0.5,0,1.2,0.2,1.7,0.4 c0.6,0.2,1.1,0.3,1.7,0.5c1.1,0.4,2.1,0.9,3.1,1.4c2.4,1.3,4.6,3.1,6.4,5c2,2.1,3.7,4.6,5.1,7.2c1.4,2.5,2.5,5.2,3.4,7.9 c1,3,1.8,6,2.3,9.1c0.6,3.1,0.9,6.2,1.2,9.4C210.8,60.6,210.7,66.5,210.2,72.4z"/> <path d="M180.3,54.4v3l0.6-0.1c0,0,0.1,0,0.3,0c0.3,0,0.9,0.1,1.3,0.5c0.4,0.4,0.5,1,0.3,1.8c0,0-6.1,26.3-7.2,31.3 C174.3,84.6,167,50,167,50l0-0.1h-1.4l0,0.2c0,0-5.2,33.7-6.3,40.4c-1.4-5.8-7.2-30.8-7.2-30.8c0-0.2,0-0.3,0-0.5 c0-0.7,0.2-1.2,0.5-1.5c0.4-0.4,1.1-0.4,1.2-0.4l0.6,0.1l0-2.9h-10.1v2.9l0.4,0.1c0.2,0,1.4,0.3,1.5,1.4c0,0,11.9,51,12.4,53.1 l0,0.1h1.8l0-0.2c0.1-0.4,4.9-32,5.8-37.9c1.1,5.9,7.3,37.5,7.4,37.9l0,0.1h1.6L187,58.7c0.3-1.1,1.2-1.2,1.6-1.2c0.1,0,0.1,0,0.1,0 l0.6,0v-3.1H180.3z"/> </svg> </a><a href="https://www.wisconsin.edu/" class="uw-footer-stand-out-link">Part of the Universities of Wisconsin</a></div> </div> <div class="uw-footer-contact"> <h3 class="uw-footer-header">Contact Us</h3><ul class="uw-contact-list"><li class="uw-contact-item uw-contact-address">Physics Department<br /> 2320 Chamberlin Hall<br /> 1150 University Avenue<br /> Madison, WI 53706-1390<br /> </li> <li class="uw-contact-item uw-contact-map-link"> <a href="/department/visit/">Map<svg class="uw-map-marker" viewBox="0 0 585 1024" version="1.1" role="img" focusable="false" aria-labelledby="dynid67501fbee899d6.68696558"> <title id="dynid67501fbee899d6.68696558">map marker</title> <path class="path1" d="M438.857 365.714q0-60.571-42.857-103.429t-103.429-42.857-103.429 42.857-42.857 103.429 42.857 103.429 103.429 42.857 103.429-42.857 42.857-103.429zM585.143 365.714q0 62.286-18.857 102.286l-208 442.286q-9.143 18.857-27.143 29.714t-38.571 10.857-38.571-10.857-26.571-29.714l-208.571-442.286q-18.857-40-18.857-102.286 0-121.143 85.714-206.857t206.857-85.714 206.857 85.714 85.714 206.857z"/> </svg></a></li> <li class="uw-contact-item">Email: <a href="mailto:info@physics.wisc.edu">info@physics.wisc.edu</a></li> <li class="uw-contact-item">Phone: <a href="tel:608-262-4526">608-262-4526</a></li> <li><ul class="uw-social-icons"><li id="uw-icon-twitter" class="uw-social-icon"><a aria-label="twitter" href="https://twitter.com/UWMadPhysics"><svg class="uw-social-symbols" viewBox="0 0 512 512" version="1.1" role="img" focusable="false" aria-hidden="true" aria-labelledby="dynid67501fbee8a779.37852934"> <title id="dynid67501fbee8a779.37852934">x twitter</title> <path class="path1" d="M389.2 48h70.6L305.6 224.2 487 464H345L233.7 318.6 106.5 464H35.8L200.7 275.5 26.8 48H172.4L272.9 180.9 389.2 48zM364.4 421.8h39.1L151.1 88h-42L364.4 421.8z"/> </svg></a></li><li id="uw-icon-instagram" class="uw-social-icon"><a aria-label="instagram" href="https://instagram.com/UWMadPhysics"><svg class="uw-social-symbols" viewBox="0 0 448 512" version="1.1" role="img" focusable="false" aria-hidden="true" aria-labelledby="dynid67501fbee8b1d6.62410553"> <title id="dynid67501fbee8b1d6.62410553">instagram</title> <path class="path1" d="M224.1 141c-63.6 0-114.9 51.3-114.9 114.9s51.3 114.9 114.9 114.9S339 319.5 339 255.9 287.7 141 224.1 141zm0 189.6c-41.1 0-74.7-33.5-74.7-74.7s33.5-74.7 74.7-74.7 74.7 33.5 74.7 74.7-33.6 74.7-74.7 74.7zm146.4-194.3c0 14.9-12 26.8-26.8 26.8-14.9 0-26.8-12-26.8-26.8s12-26.8 26.8-26.8 26.8 12 26.8 26.8zm76.1 27.2c-1.7-35.9-9.9-67.7-36.2-93.9-26.2-26.2-58-34.4-93.9-36.2-37-2.1-147.9-2.1-184.9 0-35.8 1.7-67.6 9.9-93.9 36.1s-34.4 58-36.2 93.9c-2.1 37-2.1 147.9 0 184.9 1.7 35.9 9.9 67.7 36.2 93.9s58 34.4 93.9 36.2c37 2.1 147.9 2.1 184.9 0 35.9-1.7 67.7-9.9 93.9-36.2 26.2-26.2 34.4-58 36.2-93.9 2.1-37 2.1-147.8 0-184.8zM398.8 388c-7.8 19.6-22.9 34.7-42.6 42.6-29.5 11.7-99.5 9-132.1 9s-102.7 2.6-132.1-9c-19.6-7.8-34.7-22.9-42.6-42.6-11.7-29.5-9-99.5-9-132.1s-2.6-102.7 9-132.1c7.8-19.6 22.9-34.7 42.6-42.6 29.5-11.7 99.5-9 132.1-9s102.7-2.6 132.1 9c19.6 7.8 34.7 22.9 42.6 42.6 11.7 29.5 9 99.5 9 132.1s2.7 102.7-9 132.1z"/> </svg></a></li><li id="uw-icon-linkedin" class="uw-social-icon"><a aria-label="linkedin" href="https://www.linkedin.com/company/uwmadphysics/"><svg class="uw-social-symbols" viewBox="0 0 448 512" version="1.1" role="img" focusable="false" aria-hidden="true" aria-labelledby="dynid67501fbee8bcd6.89060662"> <title id="dynid67501fbee8bcd6.89060662">linkedin</title> <path class="path1" d="M100.28 448H7.4V148.9h92.88zM53.79 108.1C24.09 108.1 0 83.5 0 53.8a53.79 53.79 0 0 1 107.58 0c0 29.7-24.1 54.3-53.79 54.3zM447.9 448h-92.68V302.4c0-34.7-.7-79.2-48.29-79.2-48.29 0-55.69 37.7-55.69 76.7V448h-92.78V148.9h89.08v40.8h1.3c12.4-23.5 42.69-48.3 87.88-48.3 94 0 111.28 61.9 111.28 142.3V448z"/> </svg></a></li><li id="uw-icon-youtube" class="uw-social-icon"><a aria-label="youtube" href="https://www.youtube.com/channel/UCdVkyf-M9Nu39NEEK9sGZ2g/videos"><svg class="uw-social-symbols" viewBox="0 0 576 512" version="1.1" role="img" focusable="false" aria-hidden="true" aria-labelledby="dynid67501fbee8c712.06291938"> <title id="dynid67501fbee8c712.06291938">youtube</title> <path class="path1" d="M549.655 124.083c-6.281-23.65-24.787-42.276-48.284-48.597C458.781 64 288 64 288 64S117.22 64 74.629 75.486c-23.497 6.322-42.003 24.947-48.284 48.597-11.412 42.867-11.412 132.305-11.412 132.305s0 89.438 11.412 132.305c6.281 23.65 24.787 41.5 48.284 47.821C117.22 448 288 448 288 448s170.78 0 213.371-11.486c23.497-6.321 42.003-24.171 48.284-47.821 11.412-42.867 11.412-132.305 11.412-132.305s0-89.438-11.412-132.305zm-317.51 213.508V175.185l142.739 81.205-142.739 81.201z"/> </svg></a></li></ul></li></ul></div> </div> <div class="uw-copyright"> <p>Website feedback, questions or accessibility issues: <a id="uw-website-issues-contact" href="mailto:it-staff@physics.wisc.edu">it-staff@physics.wisc.edu</a>.</p> <p>Learn more about <a href="https://accessible.wisc.edu/">accessibility at UW–Madison</a>.</p> <p>This site was built using the <a href="https://uwtheme.wordpress.wisc.edu/">UW Theme</a> | <a href="https://www.wisc.edu/privacy-notice/">Privacy Notice</a> | &copy; 2024 Board of Regents of the <a href="https://www.wisconsin.edu">University of Wisconsin System.</a> </p> </div> </footer> <!-- Instagram Feed JS --> <script type="text/javascript"> var sbiajaxurl = "https://www.physics.wisc.edu/wp-admin/admin-ajax.php"; </script> <script> var e = document.getElementsByClassName("uw-global-bar"); var site_url = "https://www.physics.wisc.edu"; if( e.length ) { var breadcrumbs = '<span class="website-breadcrumbs"> : <a class="uw-global-name-link" href="https://www.physics.wisc.edu">physics</a>'; // add a link to the top site for this domain (e.g. www.hep.wisc.edu) var domain_re = /.*:\/\/([^\/]*)/; var match = domain_re.exec(site_url); if( match.length > 1 ) { var domain = match[1]; var domain_parts = domain.split("."); var site_part = 0; if( domain_parts[site_part] == "www" ) site_part += 1; if( domain_parts[site_part] == "wp" ) site_part += 1; if( domain_parts[site_part] == "home" ) site_part += 1; if( domain_parts[site_part] != "physics" ) { breadcrumbs += ' : <a class="uw-global-name-link" href="https://' + domain + '">' + domain_parts[site_part] + '</a>'; } } // add a link to this sub-site (e.g. www.hep.wisc.edu/cms) var n = site_url.lastIndexOf("/"); var subsite = site_url.substr(n+1); if( subsite.lastIndexOf(".") < 0 ) { breadcrumbs += ' : <a class="uw-global-name-link" href="' + site_url + '">' + subsite + '</a>'; } e[0].innerHTML = "<span>" + e[0].innerHTML + breadcrumbs + "</span></span>"; } </script> <script> var menu; menu = document.getElementById('menu-item-3698'); if( menu ) { var html = menu.innerHTML; if( html.indexOf("Graduate") >= 0 ) { menu.innerHTML = html.replace("Graduate","Grad<span class='show-for-large show-for-stacked'>uate</span>"); } } menu = document.getElementById('menu-item-3188'); if( menu ) { var html = menu.innerHTML; if( html.indexOf("Undergraduate") >= 0 ) { menu.innerHTML = html.replace("Undergraduate","Undergrad<span class='show-for-large show-for-stacked'>uate</span>"); } } </script><script src="https://www.physics.wisc.edu/wp-content/themes/uw-theme/dist/js/jquery/jquery.min.js?ver=3.6.0" id="jquery-js"></script> <script src="https://www.physics.wisc.edu/wp-includes/js/jquery/ui/effect.min.js?ver=1.13.3" id="jquery-effects-core-js"></script> <script src="https://www.physics.wisc.edu/wp-includes/js/jquery/ui/effect-slide.min.js?ver=1.13.3" id="jquery-effects-slide-js"></script> <script src="https://www.physics.wisc.edu/wp-includes/js/jquery/ui/effect-highlight.min.js?ver=1.13.3" id="jquery-effects-highlight-js"></script> <script src="https://www.physics.wisc.edu/wp-includes/js/jquery/ui/effect-fold.min.js?ver=1.13.3" id="jquery-effects-fold-js"></script> <script src="https://www.physics.wisc.edu/wp-includes/js/jquery/ui/effect-blind.min.js?ver=1.13.3" id="jquery-effects-blind-js"></script> <script id="bg-show-hide-script-js-extra"> var BG_SHCE_USE_EFFECTS = "0"; var BG_SHCE_TOGGLE_SPEED = "400"; var BG_SHCE_TOGGLE_OPTIONS = "none"; var BG_SHCE_TOGGLE_EFFECT = "blind"; </script> <script src="https://www.physics.wisc.edu/wp-content/plugins/show-hidecollapse-expand/assets/js/bg-show-hide.js?ver=6.7.1" id="bg-show-hide-script-js"></script> <!--[if lt IE 10]> <script src="https://www.physics.wisc.edu/wp-content/themes/uw-theme/dist/js/polyfills/classList.js?ver=1.0.0" id="uwmadison-ie-js"></script> <![endif]--> <script src="https://www.physics.wisc.edu/wp-content/themes/uw-theme/dist/main.min.js?ver=1.35.1" id="uwmadison-script-js"></script> <script src="https://www.physics.wisc.edu/wp-content/themes/uw-theme/dist/js/jquery-migrate/jquery-migrate.min.js?ver=3.4.0" id="jquery-migrate-js"></script> <script src="https://cdn.wisc.cloud/cookie-consent/1.1.0/uwcookieconsent.min.js?ver=1.1.0" id="uw-cookie-consent-js"></script> <script id="uw-cookie-consent-js-after"> window.addEventListener("load", function(){window.cookieconsent.initialize()}); </script> </body> </html>

Pages: 1 2 3 4 5 6 7 8 9 10