Orbital is a degree of freedom independent of charge and spin, which plays an important role in transition metal oxides. Orbital physics is characterized by orbital degeneracy and spatial anisotropy. The recent progress of cold atom physics has provided another exciting opportunity to investigate orbital physics with both cold bosons and fermions in optical lattices. In this talk, we will present new features of orbital physics in the high orbital bands, which are not usually realized in solid state orbital systems. For bosons, the ferro-orbital interactions lead to a class of novel superfluid states with complex-valued wavefunctions breaking time reversal symmetry. These states are beyond Feynman's celebrated argument of the positive-definitiveness of many-body ground state wavefunctions for bosons. For fermions, the honeycomb lattice with the p$_x,y$-orbitals exhibits the flat band structure and the consequential non-perturbative strong correlation effects (e.g. Wigner crystallization) which is distinct from the graphene physics characterized by the p$_z$-orbital. The orbital exchange physics in the Mott-insulating states exhibits strong frustrations and provides a promising direction to realize the orbital liquid state. The experimental realization and detection of these exotic states of matter will also be discussed.

References

1) Congjun Wu, "Orbital orderings and frustrations of p-band systems in optical lattices", arxiv:08010888.

2) Congjun Wu , and S. Das Sarma, "The $p_{x,y}$-orbital counterpart of graphene: cold atoms in the honeycomb optical lattice", arXiv:0712.4284 .

3) Congjun Wu, Doron Bergman, Leon Balents, and Sankar Das Sarma, "Flat bands and Wigner crystallization in the honeycomb optical lattice", Phys. Rev. Lett. 99, 70401 (2007)

4) Congjun Wu, W. Vincent Liu, Joel Moore, and Sankar Das Sarma, "Predicted quantum stripe ordering in optical lattices" Phys. Rev. Lett. 97, 190406 (2006).

5) W. Vincent Liu, and Congjun Wu, "Atomic matter of nonzero-momentum Bose-Einstein condensation and orbital current order", Phys. Rev. A 74 , 13607 (2006).