P-wave Superfluidity by Blockade Effects in a Rydberg-Dressed Fermi Gas

We systematically investigate the p-wave superfluidity of a Rydberg-dressed Fermi gas, where the soft-core effective interaction is of finite radius $R_{c}$ due to blockade effects. After solving the BCS gap equation and comparing the free energy, we obtain the quantum phase diagram, which is composed of three different phases: polar ($p_{z}$), axial ($p_{x}+ip_{y}$), and axi-planar ($p_{x}+i\beta_{p}p_{y}$) phases. The tri-critical point locates around $R_{c}k_{F}\sim1$, where $k_{F}$ is the Fermi wave vector. We further derive the Ginzburg-Landau theory to explain the phase diagram, and estimate the transition temperature to be about 0.1$E_{F}$ in the current experimental regime of $^{6}$Li. Our work paves the way for future studies on p-wave superfluids and related quantum phase transitions in ultracold atoms.