We investigate the effects of many-body correlations on the ground-state properties of a single component ultra-cold Rydberg-dressed Fermi liquid with purely repulsive inter-particle interactions, in both three and two spatial dimensions. We have emp
loyed the Fermi-hypernetted-chain Euler-Lagrange approximation and observed that the contribution of the correlation energy on the ground-state energy becomes significant at intermediate values of the soft-core radius and large coupling strengths. For small and large soft-core radii, the correlation energy is negligible and the ground-state energy approaches the Hartree-Fock value. The positions of the main peaks in static structure factor and pair distribution function in the homogeneous fluid phase signal the formation of quantum droplet crystals with several particles confined inside each droplet.
Strong particle-plasmon interaction in electronic systems can lead to composite emph{hole-plasmon} excitations. We investigate the emergence of similar composite quasiparticles in ultracold dipolar Fermi liquids originating from the long-range dipole
-dipole interaction. We use the $G_0W$ technique with an effective interaction obtained from the static structure factor to calculate the quasiparticle properties and single-particle spectral function. We first demonstrate that within this formalism a very good agreement with the quantum Monte Carlo results could be achieved over a wide range of coupling strengths for the renormalization constant and effective mass. The composite textit{quasiparticle-zero sound} excitations which are undamped at long wavelengths emerge at intermediate and strong couplings in the spectral function and should be detectable through the radio frequency spectroscopy of nonreactive polar molecules at high densities.
We investigate the ground-state properties and the collective modes of a two-dimensional two-component Rydberg-dressed Fermi liquid in the dipole-blockade regime. We find instability of the homogeneous system toward phase separated and density ordere
d phases, using the Hartree-Fock and random-phase approximations, respectively. The spectral weight of collective density oscillations in the homogenous phase also signals the emergence of density-wave instability. We examine the effect of exchange-hole on the density-wave instability and on the collective mode dispersion using the Hubbard local-field factor.
