Stabilization of the p-wave superfluid state in an optical lattice

It is hard to stabilize the $p$-wave superfluid state of cold atomic gas in free space due to inelastic collisional losses. We consider the $p$-wave Feshbach resonance in an optical lattice, and show that it is possible to have a stable $p$-wave superfluid state where the multi-atom collisional loss is suppressed through the quantum Zeno effect. We derive the effective Hamiltonian for this system, and calculate its phase diagram in a one-dimensional optical lattice. The results show rich phase transitions between the $p$-wave superfluid state and different types of insulator states induced either by interaction or by dissipation.