Two-dimensional paired topological superfluids of Rydberg Fermi gases

We systematically investigate the topological properties of spin polarized Rydberg-dressed fermionic atoms loaded in a bilayer optical lattice. Through tuning Rydberg coupling strength and interlayer tunneling amplitude, we identify different types superfluid states generated from pairing relative phase modulation coupled two-dimensional $p$-wave superfluids. These phases include gapped/gapless with/without time-reversal symmetry. One most interesting is gapless paired with both symmetry particle-hole symmetry, which realization DIII superconductor. The flexibility experimental manipulation such systems therefore becomes promising system for realizing