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New features of orbital physics with cold bosons and fermions in optical lattices

Optical lattices with cold atoms have become a new frontier for exploring interesting physics in strongly correlated systems. In particular, recent experiments on high orbital bands provide a wonderful new opportunity for studying orbital physics, which is characterized by orbital degeneracy and spatial anisotropy. In this work, we study new features of orbital physics in the $p$-orbital bands with bosons and fermions, which are not usually realized in solid state systems. These include bosonic superfluid states breaking time reversal symmetry, quantum stripe ordering of orbital angular momentum moments in the triangular lattice,and Wigner crystallization of neutral atoms in the flat band of the honeycomb lattice. Signatures of these states are predicted and can be tested in time of flight spectra.