Quantum phase transitions of Rydberg-dressed Fermi gases Daw-Wei Wang ^{1*}^{1}Physics, National Tsing Hua University, Hsinchu, Taiwan^{2}Physics Division, National Center for Theoretical Sciences, Hsinchu, Taiwan* presenting author:Daw-Wei Wang, email:dawwei.wang@gmail.com We theoretical investigate the quantum phase diagrams of a single component Fermi gas, which is weakly coupled to a Rydberg state by a two photon transition. The effective interaction can be either repulsive or attractive with a finite soft core radius via blockade effect. For the attractive case, we systematically study the p-wave superfluidity, and obtain the quantum phase diagram of three different symmetries in the pairing wavefunction: polar, axial, and axi-planar phases. The last one is shown to be stabilized by the finite ranged nature of the effective interaction. The transition temperature is estimated to be about 0.1EF in the current experimental regime of Li⁶. For the repulsive case, we calculate the collective mode dispersion as well as the density-density correlation function. We find a roton-like minimum in the collective mode and it becomes softened when the blockade radius is large enough, leading to an instability toward a charge-density wave order in a continuous space by breaking rotational
and translation symmetries. We further compare it with the Pomeranchuk instability in condensed matter system and discuss the possible experimental parameter regime for these quantum phase transitions. Keywords: cold atoms, Rydberg gas, superfluid, charge density waves |