p-Wave Superfluid Phases of Fermi Molecules in a Bilayer Lattice Array

The superfluid p=px+ipy phases in an ultracold gas of dipolar Fermi molecules lying in two parallel square lattices in 2D are investigated. As shown by a two-body study, dipole moments oriented in opposite directions in each layer are the key ingredients in our mean-field analysis from which unconventional superfluidity is predicted. The T=0 phase diagram summarizes our findings: stable and metastable superfluid phases appear as a function of both, the dipole-dipole interaction coupling parameter and filling factor. A first-order phase transition, and thus a mixture of superfluid phases at different densities, is revealed from the coexistence curves in the metastable region. The model predicts that these superfluid phases can be observed experimentally at 10 nK in molecules of NaK confined in optical lattices of size a=532 nm. Other routes to reach higher temperatures require the use of subwavelength confinement technique.