MULTI-BAND BOSE HUBBARD MODELS AND EFFECTIVE THREE-BODY INTERACTIONS

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dc.contributor.advisorTiesinga, Eiteen_US
dc.contributor.authorPaul, Saurabhen_US
dc.contributor.departmentPhysicsen_US
dc.contributor.publisherDigital Repository at the University of Marylanden_US
dc.contributor.publisherUniversity of Maryland (College Park, Md.)en_US
dc.date.accessioned2016-09-03T05:40:32Z
dc.date.available2016-09-03T05:40:32Z
dc.date.issued2016en_US
dc.description.abstractExperiments with ultracold atoms in optical lattice have become a versatile testing ground to study diverse quantum many-body Hamiltonians. A single-band Bose-Hubbard (BH) Hamiltonian was first proposed to describe these systems in 1998 and its associated quantum phase-transition was subsequently observed in 2002. Over the years, there has been a rapid progress in experimental realizations of more complex lattice geometries, leading to more exotic BH Hamiltonians with contributions from excited bands, and modified tunneling and interaction energies. There has also been interesting theoretical insights and experimental studies on “un- conventional” Bose-Einstein condensates in optical lattices and predictions of rich orbital physics in higher bands. In this thesis, I present our results on several multi- band BH models and emergent quantum phenomena. In particular, I study optical lattices with two local minima per unit cell and show that the low energy states of a multi-band BH Hamiltonian with only pairwise interactions is equivalent to an effec- tive single-band Hamiltonian with strong three-body interactions. I also propose a second method to create three-body interactions in ultracold gases of bosonic atoms in a optical lattice. In this case, this is achieved by a careful cancellation of two contributions in the pair-wise interaction between the atoms, one proportional to the zero-energy scattering length and a second proportional to the effective range. I subsequently study the physics of Bose-Einstein condensation in the second band of a double-well 2D lattice and show that the collision aided decay rate of the con- densate to the ground band is smaller than the tunneling rate between neighboring unit cells. Finally, I propose a numerical method using the discrete variable repre- sentation for constructing real-valued Wannier functions localized in a unit cell for optical lattices. The developed numerical method is general and can be applied to a wide array of optical lattice geometries in one, two or three dimensions.en_US
dc.identifierhttps://doi.org/10.13016/M2HJ63
dc.identifier.urihttp://hdl.handle.net/1903/18586
dc.language.isoenen_US
dc.subject.pqcontrolledCondensed matter physicsen_US
dc.subject.pqcontrolledAtomic physicsen_US
dc.subject.pqcontrolledQuantum physicsen_US
dc.subject.pquncontrolledBose-Einstein condensationen_US
dc.subject.pquncontrolledMott insulatoren_US
dc.subject.pquncontrolledoptical latticeen_US
dc.subject.pquncontrolledsuperfluiden_US
dc.subject.pquncontrolledthree-body interactionen_US
dc.subject.pquncontrolledWannier functionsen_US
dc.titleMULTI-BAND BOSE HUBBARD MODELS AND EFFECTIVE THREE-BODY INTERACTIONSen_US
dc.typeDissertationen_US

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