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Orbital phases of fermions in an asymmetric optical ladder

We study a quantum ladder of interacting fermions with coupled s and p orbitals. Such a model describes dipolar molecules or atoms loaded into a double-well optical lattice, dipole moments being aligned by an external field. The two orbital components have distinct hoppings. The tunneling between them is equivalent to a partial Rashba spin-orbital coupling when the orbital space (s, p) is identified as spanned by pseudo-spin 1/2 states. A rich phase diagram, including incommensurate orbital density wave, pair density wave and other exotic superconducting phases, is proposed with bosonization analysis. In particular, superconductivity is found in the repulsive regime.