{"id":385439,"date":"2017-05-22T06:41:04","date_gmt":"2017-05-22T13:41:04","guid":{"rendered":"https:\/\/www.microsoft.com\/en-us\/research\/?post_type=msr-research-item&#038;p=385439"},"modified":"2018-10-16T20:11:22","modified_gmt":"2018-10-17T03:11:22","slug":"observing-properties-interacting-homogeneous-bose-einstein-condensate-heisenberg-limited-momentum-spread-interaction-energy-free-expansion-dynamics","status":"publish","type":"msr-research-item","link":"https:\/\/www.microsoft.com\/en-us\/research\/publication\/observing-properties-interacting-homogeneous-bose-einstein-condensate-heisenberg-limited-momentum-spread-interaction-energy-free-expansion-dynamics\/","title":{"rendered":"Observing Properties Of An Interacting Homogeneous Bose-Einstein Condensate: Heisenberg-Limited Momentum Spread, Interaction Energy, And Free-Expansion Dynamics"},"content":{"rendered":"<p>We study the properties of an atomic Bose\u2013Einstein condensate produced in an optical-box potential, using high-resolution Bragg spectroscopy. For a range of box sizes, up to <span class=\"aps-inline-formula\"><span id=\"MathJax-Element-1-Frame\" class=\"mjx-chtml MathJax_CHTML\"><span id=\"MJXc-Node-1\" class=\"mjx-math\"><span id=\"MJXc-Node-2\" class=\"mjx-mrow\"><span id=\"MJXc-Node-3\" class=\"mjx-mrow\"><span id=\"MJXc-Node-4\" class=\"mjx-mn\"><span class=\"mjx-char MJXc-TeX-main-R\">70<\/span><\/span><span id=\"MJXc-Node-5\" class=\"mjx-mspace\"><\/span><span id=\"MJXc-Node-6\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\">\u03bc<\/span><\/span><\/span><\/span><\/span><\/span> <\/span>m, we directly observe Heisenberg-limited momentum uncertainty of the condensed atoms. We measure the condensate interaction energy with a precision of <span class=\"aps-inline-formula\"><span id=\"MathJax-Element-2-Frame\" class=\"mjx-chtml MathJax_CHTML\"><span id=\"MJXc-Node-7\" class=\"mjx-math\"><span id=\"MJXc-Node-8\" class=\"mjx-mrow\"><span id=\"MJXc-Node-9\" class=\"mjx-mrow\"><span id=\"MJXc-Node-10\" class=\"mjx-msub\"><span class=\"mjx-base\"><span id=\"MJXc-Node-11\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\">k<\/span><\/span><\/span><span class=\"mjx-sub\"><span id=\"MJXc-Node-12\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-main-R\">B<\/span><\/span><\/span><\/span><span id=\"MJXc-Node-13\" class=\"mjx-mo MJXc-space2\"><span class=\"mjx-char MJXc-TeX-main-R\">\u00d7<\/span><\/span><span id=\"MJXc-Node-14\" class=\"mjx-mn MJXc-space2\"><span class=\"mjx-char MJXc-TeX-main-R\">100<\/span><\/span><\/span><\/span><\/span><\/span> <\/span> pK and study, both experimentally and numerically, the dynamics of its free expansion upon release from the box potential. All our measurements are in good agreement with theoretical expectations for a perfectly homogeneous condensate of spatial extent equal to the size of the box, which also establishes the uniformity of our optical-box system on a sub-nK energy scale.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>We study the properties of an atomic Bose\u2013Einstein condensate produced in an optical-box potential, using high-resolution Bragg spectroscopy. For a range of box sizes, up to 70\u03bc m, we directly observe Heisenberg-limited momentum uncertainty of the condensed atoms. We measure the condensate interaction energy with a precision of kB\u00d7100 pK and study, both experimentally and [&hellip;]<\/p>\n","protected":false},"featured_media":0,"template":"","meta":{"msr-url-field":"","msr-podcast-episode":"","msrModifiedDate":"","msrModifiedDateEnabled":false,"ep_exclude_from_search":false,"_classifai_error":"","msr-author-ordering":null,"msr_publishername":"","msr_publisher_other":"","msr_booktitle":"","msr_chapter":"","msr_edition":"","msr_editors":"","msr_how_published":"","msr_isbn":"","msr_issue":"","msr_journal":"Phys. Rev. A","msr_number":"","msr_organization":"","msr_pages_string":"061604(R)","msr_page_range_start":"","msr_page_range_end":"","msr_series":"","msr_volume":"89","msr_copyright":"","msr_conference_name":"","msr_doi":"https:\/\/doi.org\/10.1103\/PhysRevA.89.061604","msr_arxiv_id":"","msr_s2_paper_id":"","msr_mag_id":"","msr_pubmed_id":"","msr_other_authors":"","msr_other_contributors":"","msr_speaker":"","msr_award":"","msr_affiliation":"","msr_institution":"","msr_host":"","msr_version":"","msr_duration":"","msr_original_fields_of_study":"","msr_release_tracker_id":"","msr_s2_match_type":"","msr_citation_count_updated":"","msr_published_date":"2014-06-30","msr_highlight_text":"","msr_notes":"","msr_longbiography":"","msr_publicationurl":"https:\/\/journals.aps.org\/pra\/abstract\/10.1103\/PhysRevA.89.061604","msr_external_url":"","msr_secondary_video_url":"","msr_conference_url":"","msr_journal_url":"","msr_s2_pdf_url":"","msr_year":0,"msr_citation_count":0,"msr_influential_citations":0,"msr_reference_count":0,"msr_s2_match_confidence":0,"msr_microsoftintellectualproperty":true,"msr_s2_open_access":false,"msr_s2_author_ids":[],"msr_pub_ids":[],"msr_hide_image_in_river":0,"footnotes":""},"msr-research-highlight":[],"research-area":[13552],"msr-publication-type":[193715],"msr-publisher":[],"msr-focus-area":[],"msr-locale":[268875],"msr-post-option":[],"msr-field-of-study":[],"msr-conference":[],"msr-journal":[],"msr-impact-theme":[],"msr-pillar":[],"class_list":["post-385439","msr-research-item","type-msr-research-item","status-publish","hentry","msr-research-area-hardware-devices","msr-locale-en_us"],"msr_publishername":"","msr_edition":"","msr_affiliation":"","msr_published_date":"2014-06-30","msr_host":"","msr_duration":"","msr_version":"","msr_speaker":"","msr_other_contributors":"","msr_booktitle":"","msr_pages_string":"061604(R)","msr_chapter":"","msr_isbn":"","msr_journal":"Phys. 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