{"id":608063,"date":"2017-10-24T02:00:00","date_gmt":"2017-10-23T23:00:00","guid":{"rendered":"http:\/\/www.fyysika.ee\/?guid=3cdd66150e83561cbe9ae354bc379e29"},"modified":"2017-10-24T02:00:00","modified_gmt":"2017-10-23T23:00:00","slug":"tight-binding-tunneling-amplitude-of-an-optical-lattice","status":"publish","type":"post","link":"https:\/\/www.fyysika.ee\/?p=608063","title":{"rendered":"Tight-binding tunneling amplitude of an optical lattice"},"content":{"rendered":"<p>The particle in a periodic potential is an important topic in an undergraduate quantum mechanics<br \/>\ncurriculum and a stepping stone on the way to more advanced topics, such as courses on interacting<br \/>\nelectrons in crystalline solids, and graduate-level research in solid-state and condensed matter<br \/>\nphysics. The interacting many-body phenomena are usually described in terms of the second quantized<br \/>\nlattice Hamiltonians which treat single-particle physics on the level of tight-binding approximation<br \/>\nand add interactions on top of it. The aim of this paper is to show how the tight-binding tunneling<br \/>\namplitude can be related to the strength of the periodic potential for the case of a cosine<br \/>\npotential used in the burgeoning field of ultracold atoms. We show how to approach the problem of<br \/>\ncomputing the tunneling amplitude of a deep lattice using the JWKB<br \/>\n(Jeffreys\u2013Wentzel\u2013Kramers\u2013Brillouin, also known as semiclassical) approximation. We also point out<br \/>\nthat care should be taken when applying the&#8230;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>The particle in a periodic potential is an important topic in an undergraduate quantum mechanics<br \/>\ncurriculum and a stepping stone on the way to more advanced topics, such as courses on interacting<br \/>\nelectrons in crystalline solids, and graduate-level re&#8230;<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_genesis_hide_title":false,"_genesis_hide_breadcrumbs":false,"_genesis_hide_singular_image":false,"_genesis_hide_footer_widgets":false,"_genesis_custom_body_class":"","_genesis_custom_post_class":"","_genesis_layout":"","footnotes":""},"categories":[178],"tags":[],"class_list":{"0":"post-608063","1":"post","2":"type-post","3":"status-publish","4":"format-standard","6":"category-rss-fuusikaharidus","7":"entry"},"_links":{"self":[{"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/posts\/608063","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=608063"}],"version-history":[{"count":0,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/posts\/608063\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=608063"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=608063"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=608063"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}