The kaleidoscope of phases in one-dimensional Rydberg dressed Fermi gases

We theoretically investigate the ground state phases of a Rydberg-dressed Fermi gas in a one-dimensional optical lattice. The asymptotic low energy behavior of the system is calculated with bosonization (for weak interactions) and a strong coupling expansion (for strong Rydberg dressing), and both are verified with density matrix renormalization group calculations. The dressed Rydberg system has an attractive backscattering interaction for a certain momentum range, which can be directly controlled by tuning the filling. This results in quasi-long range ordered phases alternating as a function of fermion density, when the interaction is weak. In contrast, the strong interactions are governed by the commensurate charge-density wave states, similar to the PXP-model in Rydberg systems. We present the phase diagram interpolating both limits, and discuss the experimental implications.