Ultracold gases in non-Abelian synthetic gauge fields

thesis
dc.abstract.enThe focus of this thesis is in the area of Abelian and non-Abelian gauge fields th a t can be efficiently simulated in ultracold atomic systems. These exotic fields and their impact on fermionic particles is studied in the context of two-dimensional systems mainly in optical lattices, th a t also are available with current experimental techniques. Behaviour of a particle under the influence of such non-Abelian gauge field is contrasted with the standard case of homogeneous magnetic field. Its spectrum and the transport properties such as quantum Hall effect are investigated. The conditions for the energy bands to form a Hofstadter-butterfly-like gaps in a non-Abelian field are given. We show th a t as long as the Wilson loop for the field is constant, its non-Abelian character does not destroy the big gaps and hence, allows for the integer quantum Hall effect (IQHE). A family of new butterfly spectra is found and the modified IQHE is calculated with the use of Chern numbers. Further, the spectrum of the system is studied in detail and it is demonstrated th a t it can exhibit anomalies i.e. Dirac cones. The elementary excitations of a system with such spectrum are massless fermions traveling with a modified speed of light similarly to the Majorana fermions in the graphene described by the Dirac equation. We further show th a t in the case of synthetic non-Abelian gauge field these cones can be squeezed and the speed of light then depends on the direction. Under the conditions of such squeezing the interactions are considered and the first steps towards the analysis of the Fractional quantum Hall effect (FQHE) in the presence of non-Abelian field are done. The matrix elements of the interaction matrix are analytically calculated.pl
dc.affiliationWydział Fizyki, Astronomii i Informatyki Stosowanej : Instytut Fizyki im. Mariana Smoluchowskiegopl
dc.contributor.advisorLewenstein, Maciejpl
dc.contributor.advisorZakrzewski, Jakub - 100023 pl
dc.contributor.authorKubasiak, Annapl
dc.contributor.institutionInstitute of Photonic Sciencespl
dc.contributor.reviewerJuzeliūnas, Gediminaspl
dc.contributor.reviewerSacha, Krzysztof - 100749 pl
dc.date.accession2018-04-25pl
dc.date.accessioned2018-04-26T10:03:39Z
dc.date.available2018-04-26T10:03:39Z
dc.date.openaccess0
dc.date.submitted2011-09-02pl
dc.description.accesstimew momencie opublikowania
dc.description.additionalDostęp do publikacji jest możliwy w Archiwum UJpl
dc.description.physicalXIV, 130pl
dc.description.versionostateczna wersja autorska (postprint)
dc.identifier.callnumberDokt. 2011/158pl
dc.identifier.urihttps://ruj.uj.edu.pl/xmlui/handle/item/53919
dc.identifier.weblinkhttp://www.fais.uj.edu.pl/documents/41628/a4291db0-dfe1-4fed-8c9b-d2c47cea5868pl
dc.languageengpl
dc.place[Castelldefels]pl
dc.rightsCopyright*
dc.rights.licenceInna otwarta licencja
dc.rights.urihttp://ruj.uj.edu.pl/4dspace/License/copyright/licencja_copyright.pdf*
dc.share.typeinne
dc.subject.enHall effectpl
dc.subject.ennonabelianpl
dc.subject.enoptical latticespl
dc.subject.plefekt Hallapl
dc.subject.plnieabelowepl
dc.subject.plsieci optycznepl
dc.titleUltracold gases in non-Abelian synthetic gauge fieldspl
dc.title.alternativeUltrazimne gazy atomowe w nieabelowych sztucznych polach cechowaniapl
dc.typeThesispl
dspace.entity.typePublication
dc.abstract.enpl
The focus of this thesis is in the area of Abelian and non-Abelian gauge fields th a t can be efficiently simulated in ultracold atomic systems. These exotic fields and their impact on fermionic particles is studied in the context of two-dimensional systems mainly in optical lattices, th a t also are available with current experimental techniques. Behaviour of a particle under the influence of such non-Abelian gauge field is contrasted with the standard case of homogeneous magnetic field. Its spectrum and the transport properties such as quantum Hall effect are investigated. The conditions for the energy bands to form a Hofstadter-butterfly-like gaps in a non-Abelian field are given. We show th a t as long as the Wilson loop for the field is constant, its non-Abelian character does not destroy the big gaps and hence, allows for the integer quantum Hall effect (IQHE). A family of new butterfly spectra is found and the modified IQHE is calculated with the use of Chern numbers. Further, the spectrum of the system is studied in detail and it is demonstrated th a t it can exhibit anomalies i.e. Dirac cones. The elementary excitations of a system with such spectrum are massless fermions traveling with a modified speed of light similarly to the Majorana fermions in the graphene described by the Dirac equation. We further show th a t in the case of synthetic non-Abelian gauge field these cones can be squeezed and the speed of light then depends on the direction. Under the conditions of such squeezing the interactions are considered and the first steps towards the analysis of the Fractional quantum Hall effect (FQHE) in the presence of non-Abelian field are done. The matrix elements of the interaction matrix are analytically calculated.
dc.affiliationpl
Wydział Fizyki, Astronomii i Informatyki Stosowanej : Instytut Fizyki im. Mariana Smoluchowskiego
dc.contributor.advisorpl
Lewenstein, Maciej
dc.contributor.advisorpl
Zakrzewski, Jakub - 100023
dc.contributor.authorpl
Kubasiak, Anna
dc.contributor.institutionpl
Institute of Photonic Sciences
dc.contributor.reviewerpl
Juzeliūnas, Gediminas
dc.contributor.reviewerpl
Sacha, Krzysztof - 100749
dc.date.accessionpl
2018-04-25
dc.date.accessioned
2018-04-26T10:03:39Z
dc.date.available
2018-04-26T10:03:39Z
dc.date.openaccess
0
dc.date.submittedpl
2011-09-02
dc.description.accesstime
w momencie opublikowania
dc.description.additionalpl
Dostęp do publikacji jest możliwy w Archiwum UJ
dc.description.physicalpl
XIV, 130
dc.description.version
ostateczna wersja autorska (postprint)
dc.identifier.callnumberpl
Dokt. 2011/158
dc.identifier.uri
https://ruj.uj.edu.pl/xmlui/handle/item/53919
dc.identifier.weblinkpl
http://www.fais.uj.edu.pl/documents/41628/a4291db0-dfe1-4fed-8c9b-d2c47cea5868
dc.languagepl
eng
dc.placepl
[Castelldefels]
dc.rights*
Copyright
dc.rights.licence
Inna otwarta licencja
dc.rights.uri*
http://ruj.uj.edu.pl/4dspace/License/copyright/licencja_copyright.pdf
dc.share.type
inne
dc.subject.enpl
Hall effect
dc.subject.enpl
nonabelian
dc.subject.enpl
optical lattices
dc.subject.plpl
efekt Halla
dc.subject.plpl
nieabelowe
dc.subject.plpl
sieci optyczne
dc.titlepl
Ultracold gases in non-Abelian synthetic gauge fields
dc.title.alternativepl
Ultrazimne gazy atomowe w nieabelowych sztucznych polach cechowania
dc.typepl
Thesis
dspace.entity.type
Publication
Affiliations

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