{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/34226"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/34226","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Crystalline and glassy states of ultracold atomic systems","abstract":"\"Spatially modulated ordered states, such as crystals, liquid crystals, and antiferromagnets, are ubiquitous in nature but relatively difficult to realize in ultracold atomic systems. In the present work, we present a scheme for generating controllable cavity-mediated interactions between atoms, and show that these interactions give rise to a crystallization transition in the case of a transversely pumped optical cavity. We focus on the case of multimode cavities, in which the interactions are relatively local and the range of possible ordered configurations (and consequently of low-energy fluctuations) is large; as we show, the crystallization transition for a Bose-Einstein condensate in a multimode cavity is driven first-order by fluctuations, through the Brazovskii effect. The ordered state to which this crystallization transition gives rise is a \"\"supersolid,\"\" possessing both superfluid and solid order. We address the crystallization transition and the properties of the ordered state, discuss the experimental feasibility of observing these, and finally show how ordering in layered systems of atoms is geometrically frustrated. We then introduce a more straightforward realization of frustrated cavity-mediated interactions, viz. systems of randomly-positioned spins in multimode cavities. We show by means of a mapping to a variant of the Hopfield associative-memory model that such systems exhibit a spin-glass phase. Finally, we consider a different ultracold-atomic setting---that of spin-orbit-coupled Bose gases---in which the Brazovskii effect has a profound influence on the low-temperature phases, leading to a universal preference for stripe-like ordering at zero temperature and bosonic pair condensation at nonzero temperatures.\"","abstract_html":""Spatially modulated ordered states, such as crystals, liquid crystals, and antiferromagnets, are ubiquitous in nature but relatively difficult to realize in ultracold atomic systems. In the present work, we present a scheme for generating controllable cavity-mediated interactions between atoms, and show that these interactions give rise to a crystallization transition in the case of a transversely pumped optical cavity. We focus on the case of multimode cavities, in which the interactions are relatively local and the range of possible ordered configurations (and consequently of low-energy fluctuations) is large; as we show, the crystallization transition for a Bose-Einstein condensate in a multimode cavity is driven first-order by fluctuations, through the Brazovskii effect. The ordered state to which this crystallization transition gives rise is a ""supersolid,"" possessing both superfluid and solid order. We address the crystallization transition and the properties of the ordered state, discuss the experimental feasibility of observing these, and finally show how ordering in layered systems of atoms is geometrically frustrated. We then introduce a more straightforward realization of frustrated cavity-mediated interactions, viz. systems of randomly-positioned spins in multimode cavities. We show by means of a mapping to a variant of the Hopfield associative-memory model that such systems exhibit a spin-glass phase. Finally, we consider a different ultracold-atomic setting---that of spin-orbit-coupled Bose gases---in which the Brazovskii effect has a profound influence on the low-temperature phases, leading to a universal preference for stripe-like ordering at zero temperature and bosonic pair condensation at nonzero temperatures."","abstract_has_math":false,"creators":["Gopalakrishnan, Sarang"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Physics","degree_department":null,"school":null,"contributors":["Goldbart, Paul M.","Fradkin, Eduardo H.","DeMarco, Brian L.","Stack, John D."],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2012,"date_issued":"2012-09-18T21:06:46Z","date_published":"2012-09-18T21:06:46Z","updated_at":"2026-07-22T22:25:30Z","subjects":["Bose-Einstein condensates","optical cavities","spin glasses","associative memories","spin-orbit coupling","Brazovskii effect","liquid crystals","ultracold atomic systems","phase transitions","quantum criticality"],"languages":["en"],"rights":["Copyright 2012 Sarang Gopalakrishnan"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/2142/34226","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Goldbart, Paul M.","Fradkin, Eduardo H.","DeMarco, Brian L.","Stack, John D."]},{"key":"dc:creator","label":"Author","values":["Gopalakrishnan, Sarang"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2012-09-18T21:06:46Z","2012-08"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Physics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois at Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Bose-Einstein condensates","optical cavities","spin glasses","associative memories","spin-orbit coupling","Brazovskii effect","liquid crystals","ultracold atomic systems","phase transitions","quantum criticality"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2012 Sarang Gopalakrishnan"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/34226"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["\"Spatially modulated ordered states, such as crystals, liquid crystals, and antiferromagnets, are ubiquitous in nature but relatively difficult to realize in ultracold atomic systems. In the present work, we present a scheme for generating controllable cavity-mediated interactions between atoms, and show that these interactions give rise to a crystallization transition in the case of a transversely pumped optical cavity. We focus on the case of multimode cavities, in which the interactions are relatively local and the range of possible ordered configurations (and consequently of low-energy fluctuations) is large; as we show, the crystallization transition for a Bose-Einstein condensate in a multimode cavity is driven first-order by fluctuations, through the Brazovskii effect. The ordered state to which this crystallization transition gives rise is a \"\"supersolid,\"\" possessing both superfluid and solid order. We address the crystallization transition and the properties of the ordered state, discuss the experimental feasibility of observing these, and finally show how ordering in layered systems of atoms is geometrically frustrated. We then introduce a more straightforward realization of frustrated cavity-mediated interactions, viz. systems of randomly-positioned spins in multimode cavities. We show by means of a mapping to a variant of the Hopfield associative-memory model that such systems exhibit a spin-glass phase. Finally, we consider a different ultracold-atomic setting---that of spin-orbit-coupled Bose gases---in which the Brazovskii effect has a profound influence on the low-temperature phases, leading to a universal preference for stripe-like ordering at zero temperature and bosonic pair condensation at nonzero temperatures.\"","Item withdrawn by Mark Zulauf (zulauf@illinois.edu) on 2012-06-08T15:52:03Z Item was in collections: University of Illinois Theses & Dissertations (ID: 1) No. of bitstreams: 3 thesis-deposit-ver-prime.tex: 320897 bytes, checksum: 29ec771834d5e820458a7b6adad3cc8c (MD5) Gopalakrishnan_Sarang.pdf: 1511031 bytes, checksum: 27576fcf5e8d16d4ac57a2b768c35b8b (MD5) Gopalakrishnan_Sarang.pdf: 2590042 bytes, checksum: 3831579c40523f593d44f807bd1d84b4 (MD5)","Made available in DSpace on 2012-09-18T21:06:46Z (GMT). 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In the present work, we present a scheme for generating controllable cavity-mediated interactions between atoms, and show that these interactions give rise to a crystallization transition in the case of a transversely pumped optical cavity. We focus on the case of multimode cavities, in which the interactions are relatively local and the range of possible ordered configurations (and consequently of low-energy fluctuations) is large; as we show, the crystallization transition for a Bose-Einstein condensate in a multimode cavity is driven first-order by fluctuations, through the Brazovskii effect. The ordered state to which this crystallization transition gives rise is a \"\"supersolid,\"\" possessing both superfluid and solid order. We address the crystallization transition and the properties of the ordered state, discuss the experimental feasibility of observing these, and finally show how ordering in layered systems of atoms is geometrically frustrated. We then introduce a more straightforward realization of frustrated cavity-mediated interactions, viz. systems of randomly-positioned spins in multimode cavities. We show by means of a mapping to a variant of the Hopfield associative-memory model that such systems exhibit a spin-glass phase. Finally, we consider a different ultracold-atomic setting---that of spin-orbit-coupled Bose gases---in which the Brazovskii effect has a profound influence on the low-temperature phases, leading to a universal preference for stripe-like ordering at zero temperature and bosonic pair condensation at nonzero temperatures.\"","Item withdrawn by Mark Zulauf (zulauf@illinois.edu) on 2012-06-08T15:52:03Z Item was in collections: University of Illinois Theses & Dissertations (ID: 1) No. of bitstreams: 3 thesis-deposit-ver-prime.tex: 320897 bytes, checksum: 29ec771834d5e820458a7b6adad3cc8c (MD5) Gopalakrishnan_Sarang.pdf: 1511031 bytes, checksum: 27576fcf5e8d16d4ac57a2b768c35b8b (MD5) Gopalakrishnan_Sarang.pdf: 2590042 bytes, checksum: 3831579c40523f593d44f807bd1d84b4 (MD5)","Made available in DSpace on 2012-09-18T21:06:46Z (GMT). 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