Abstract/Details

Bosons in rotating optical lattices


2008 2008

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Abstract (summary)

The fractional Quantum Hall effect (FQHE) has been predicted in a cloud of bosons rotating at a frequency equal to that of the confining harmonic potential. Achieving this regime experimentally, by directly spinning the cloud, is a challenge. In this thesis, we probe an alternate approach to realizing the FQHE physics in cold gases by examining cold bosons confined to a rotating optical lattice.

We derive modified Bose-Hubbard Hamiltonians to study the system in the tight-binding limit and develop analogies to Bloch electrons in the presence of a magnetic field. The primary effect of rotation is to introduce non-abelian character in the problem. This is because the system picks up a phase not always equal to a multiple of 2π when a particle goes around a plaquette.

We numerically study hardcore bosons in the tight-binding limit by diagonalizing a Hamiltonian constructed using a truncated Fock basis. We show that vorticity can exist in the tight-binding limit though angular momentum is no longer quantized. Using the discrete rotational symmetry of the system, we identify quasi-angular momentum as a good quantum number. Quantum phase transitions are expected when the discrete rotational symmetry of the ground state changes. Using a perturbative analysis, we show that the effect of a weak lattice is to spatially modulate the Hall resistance. A linear-response analysis of the system’s response to an AC perturbation shows that the system does indeed display FQHE characteristics. We attempt to extend the analysis to larger systems using Monte Carlo methods. We show that the sign problem is inherent in the World Line Monte Carlo method as applied to non-abelian systems.

Indexing (details)


Subject
Condensation;
Atoms & subatomic particles
Classification
0611: Condensation
0748: Atoms & subatomic particles
Identifier / keyword
Pure sciences; Bose-Einstein condensation; Bose-Hubbard Hamiltonians; Bosons; Optical lattices; Rotating lattices; Rotating optical lattices; Rotation; Vortex
Title
Bosons in rotating optical lattices
Author
Bhat, Rajiv
Number of pages
153
Publication year
2008
Degree date
2008
School code
0051
Source
DAI-B 69/07, Dissertation Abstracts International
Place of publication
Ann Arbor
Country of publication
United States
ISBN
9780549672791
Advisor
Holland, Murray J.
Committee member
Bohn, John L.; Cooper, John; Cornell, Eric A.; Hamilton, Andrew; Wineland, David
University/institution
University of Colorado at Boulder
Department
Physics
University location
United States -- Colorado
Degree
Ph.D.
Source type
Dissertations & Theses
Language
English
Document type
Dissertation/Thesis
Dissertation/thesis number
3315808
ProQuest document ID
230779010
Copyright
Database copyright ProQuest LLC; ProQuest does not claim copyright in the individual underlying works.
Document URL
http://search.proquest.com/docview/230779010
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