Topological Phases of Ultracold Atoms Beyond Standard Optical Lattices

Significant experimental developments in ultracold gases, such as novel optical lattice geometries and dynamic driving, provide unprecedented opportunities to advance our understanding of many-body physics. Motivated by these developments, the proposed research carries out systematic theoretical studies on three emergent topics, each of which contains exciting unique aspects of no prior analogue in solids. The first topic is correlated and topological phases of interacting atoms on the higher orbital bands of optical lattices with non-standard geometry. The proposed research will investigate the inter-band pairing of polarized fermions, topological chiral p-wave superfluids from s-wave interaction, and correlated orbital phases by repulsive interaction. The second topic explores the topological superfluid and insulating phases of atoms in periodically driven (for instance, shaken or kicked) optical lattices. Quantitative theories will be developed to obtain the phase diagrams and experimental signatures. The third is a longer term goal, proposed to investigate a few fundamental issues in quantum dynamics including time generalization of topological invariants and whether it is quantum mechanically possible to have edge states on the time-space boundary.