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.

ABLE-BODIED WOMANHOOD: DISABILITY AND CORPOREALLY EXCLUSIONARY NARRATIVES IN BLACK AND WHITE WOMEN’S RIGHTS DISCOURSES, 1832-1932

This project is a feminist disability rhetorical analysis of US black and white women’s rights movements from 1832-1932. Guided by Disability and Feminist Theory, it works to identify the presence and use of patterns of disability tropes in women’s rights discourses. From Lucretia Coffin Mott to Sojourner Truth, Elizabeth Cady Stanton to Mary Church Terrell, and Charlotte Perkins Gilman to Addie Hunton, this project interrogates the rhetorical work of dominant narratives and lesser known voices in women’s rights discourses. I argue that early black and white women’s rights advocates often utilized and repeated a disability rhetoric that relied on disability metaphor, narrative prosthesis, and corporeally exclusionary narratives in order to construct definitions of womanhood. Their insistence on cognitive ability as a marker of “fitness” and “ability” provided the foundation for rights arguments based on ableist assumptions of autonomy and citizenship. I also argue that this use of disability rhetoric relied on and furthered a pervasive ableist ideology present not only in many of these movements, but in US society. In the process, US black and white women’s rights discourses have continually elided women with disabilities from women’s rights discourses because their bodies (physically, cognitively, and/or psychologically) did not meet the ableist prerequisites set for claiming women’s rights during this time period.