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High orbital quantum phases in optical lattices: from p-wave BEC to topological superconductivity

Recent ultra-cold gas experiments loaded alkali atoms into high orbital bands of optical lattices, where orbital degrees of freedom and degeneracy play an essential role in understanding many-body physics. I will discuss quantum phases and transitions for p-band bosons as well as for fermions. For bosons we find a time reversal symmetry broken condensate in the ground state featuring staggered orbital currents. Such staggered Ising order is also present in p-band Mott states as well. Our recent work finds that the time-reversal symmetry breaking also occurs in a fermonic system, where we have superconducting paring between s- and p-bands. This time-reversal symmetry breaking superconducting phase has finite Chern number and chiral edge states, yet not requiring spin-orbital couplings or p-wave/finite range interactions.