Center-of-mass p-wave fermionic superfluidity

We propose a new kind of pairing between two fermion species where the pairs condense at a finite momentum equal to the sum of two Fermi momenta and exhibit a $p$-wave center-of-mass wavefunction in a quasi-one dimensional system. This pairing phase is therefore related to but is fundamentally different from both the modulated superfluidity of Fulde-Ferrell-Larkin-Ovchinnikov, where the ordering wavevector is given by the Fermi mometum difference, and the usual $p$-wave superfluid such as $^3$He, where the orbital symmetry refers to the relative motion within each pair. Our numerical simulation and mean field calculation confirm that this occurs for spin imbalanced Fermi gases under a new experimental condition-- -the spin up and down Fermi levels lie within the $p_x$ and $s$ orbital bands of optical lattices, respectively.