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

Experiments 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.

Sexism and Imperialism in Mozart's Don Giovanni, Puccini's Madama Butterfly, and Blitzstein's Regina: A Performance Study

This dissertation project comprises three major operatic performances and an accompanying document; a performance study which surveys aspects of sexism and imperialism as represented in three operas written over the last three centuries by examining the implications of prejudice through research as well as through performances of the major roles found in the operas. Mr. Eversole performed the role of Sharpless in the 2014 Castleton Festival production of Madama Butterfly (music by Giacomo Puccini, libretto by Luigi Illica and Giuseppe Giacosa), conducted by Bradley Moore. In 2015, Mr. Eversole sang the title role in four performances of Mozart and Da Ponte’s Don Giovanni with the Maryland Opera Studio at the Clarice Smith Performing Arts Center, conducted by Craig Kier. Also as part of the Maryland Opera Studio 2015-16 season, Mr. Eversole appeared as Oscar Hubbard in four performances of Marc Blitzstein’s Regina, an adaptation of Lillian Hellman’s 1939 play, The Little Foxes. These performances were also conducted by Craig Kier. The accompanying research document discusses significant issues of cultural, geographical, and sexual hegemony as they relate to each opera. It examines the plots and characters of the operas from a postcolonial and feminist perspective, and takes a moral stance against imperialism, sexism, domestic abuse, and in general, the exploitation of women and of the colonized by the socially privileged and powerful. Recordings of all three operas can be accessed at the University of Maryland Hornbake Library. They are: Giacomo Puccini’s Madama Butterfly (the role of Sharpless) July 20, 2014, Castleton Festival production, Bradley Moore, Conductor Castleton, Virginia Wolfgang Amadeus Mozart’s Don Giovanni (title role) November 22nd, 2015, Maryland Opera Studio, Craig Kier, Conductor Clarice Smith Performing Arts Center, UMD Marc Blitzstein’s Regina, (Oscar Hubbard) April 8th, 8016, Maryland Opera Studio, Craig Kier, Conductor Clarice Smith Performing Arts Center, UMD