Orbital coupled dipolar fermions in an asymmetric optical ladder

We study a quantum ladder of dipolar atoms/molecules with coupled $s$ and $p$ orbitals. The interaction of such a system can be controlled with 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 is established. In particular a superconducting phase is found for repulsive fermions and a plaquette phase is found for bosons at 1/4 filling.