  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.
