Strongly Interacting Fermions in Optical Lattices and Superlattices

[摘要] This dissertation summarizes my recent work regarding systems of strongly interacting fermionic atoms in optical lattices. This work addresses the combination of two experimental techniques that have been the subject of much recent research in ultracold atom physics. One is the use of optical lattices, which provide a meansto realize diverse interaction configurations within a clean, controllable system. The other is the use of magnetically tunable Feshbach resonances to control the strength of the interatomic interaction. Together, these techniques offer the possibility of an experimental realization of many important model Hamiltonians of condensed matter physics, and may also lead to the discovery of new physics.Recent study of this system has shown that strong interactions near Feshbach resonance will lead to the population of multiple lattice bands, and that collisions between atoms on neighboring sites cannot be neglected. These effects lead to acomplicated Hamiltonian, but one which can be simplified to an effective single-band model equivalent to the generalized Hubbard model (GHM), which is an extension of the Hubbard model that includes correlated hopping terms. My main results concern the study of this model.The strong correlations between the particles make it difficult to definitively determine the many body physics of the GHM. As a first approach to understanding the GHM in optical lattices, I focus mainly on cases where the problem is greatlysimplified by allowing interactions among only small groups of lattice sites. This restriction can be implemented in experiments using an optical superlattice potential. Our results include a proposed scheme (based on double-well superlattices) to empirically verify that the GHM describes this system and to directly measure thevarious parameters of this model. Other results include exact solutions on four-site square plaquettes, which demonstrate that d-wave excitations can occur in the low-energy states. By using a superlattice to give an array of weakly coupled plaquettes, one can thus produce a d-wave superfluid state. This is of relevance to the study of high-Tc superconductors, although I note certain key differences between the sort ofd-wave superfluid described here and that of the superconductors.

[发布机构] University of Michigan

[效力级别] Optical Lattices

[关键词] Ultracold Atoms;Optical Lattices;Feshbach Resonance;Superlattices;Fermions;Physics;Science;Physics