Abstract
Rydberg-dressed quantum gas is a promising ultracold atom system, which provides highly controllable interaction and long coherence time. Here we study a Rydberg-Dressed Fermi Gas with repulsive interaction at three-dimensional free space. The interaction between Rydberg-dressed atoms has a length scale Rc introduced by the blockade eff ect, which features a notable negative minimum in momentum space. As such, calculation within random phase approximation shows that a collective mode softens in strong interaction or long blockade radius regime, indicating a quantum phase transition from a Fermi liquid to an unknown phase. By the guess that this phase is a density wave phase, we develop a mean fi eld theory to study the ground state properties (the phase diagram, critical temperature and the form of density modulation) of the system. The result shows there is a first order phase transition from the Fermi liquid phase to a rippled density wave phase with body centered cubic (BCC) structure. Furthermore, we investigate Pomeranchuk instability (PI) of our system with three diff erent methods: numerical computation of energy (fi nite distortion of Fermi surface), Ginzberg-Landau expansion and the PI condition (both are small distortion of Fermi surface). These three results consistently show that there is no PI in the system. Our finding adds an new member to the density wave phase. This new phase has lattice constant introduced by the blockade eff ect, which is diff erent from the Wigner crystal (length scale given by particle density) or charge density wave in solid states (length scale given by the underlying crystal structure).