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.

Ceramic Materials Development for Intermediate Temperature Solid Oxide Fuel Cell (IT-SOFC)

Solid oxide fuel cell (SOFC) is an electrochemical device that converts chemical energy into electric power with high efficiency. Traditional SOFC has its disadvantages, such as redox cycling instability and carbon deposition while using hydrocarbon fuels. It is because traditional SOFC uses Ni-cermet as anode. In order to solve these problems, ceramic anode is a good candidate to replace Ni. However, the conductivity of most ceramic anode materials are much lower than Ni metal, and it introduces high ohmic resistance. How to increase the conductivity is a hot topic in this research field. Based on our proposed mechanism, several types of ceramic materials have been developed. Vanadium doped perovskite, Sr1-x/2VxTi1-xO3 (SVT) and Sr0.2Na0.8Nb1-xVxO3 (SNNV), achieved the conductivity as high as 300 S*cm-1 in hydrogen, without any high temperature reduction. GDC electrolyte supported cell was fabricated with Sr0.2Na0.8Nb0.9V0.1O3 and the performance was measured in hydrogen and methane respectively. Due to vanadium’s intrinsic problems, the anode supported cell is not easy. Fe doped double perovskite Sr2CoMoO6 (SFCM) was also developed. By carefully doping Fe, the conductivity was improved over one magnitude, without any vigorous reducing conditions. SFCM anode supported cell was successfully fabricated with GDC as the electrolyte. By impregnating Ni-GDC nano particles into the anode, the cell can be operated at lower temperatures while having higher performance than the traditional Ni-cermet cells. Meanwhile, this SFCM anode supported SOFC has long term stability in the reformate containing methane. During the anode development, cathode improvement caused by a thin Co-GDC layer was observed. By adding this Co-GDC layer between the electrolyte and the cathode, the interfacial resistance decreases due to fast oxygen ion transport. This mechanism was confirmed via isotope exchange. This Co-GDC layer works with multiple kinds of cathodes and the modified cell’s performance is 3 times as the traditional Ni-GDC cell. With this new method, lowering the SOFC operation temperature is feasible.