Fermi liquid properties of ultra-cold Rydberg-dressed gases

We investigate the Landau-Fermi liquid properties such as the quasiparticle self-energy, the many-body effective mass, and the renormalization constant of a three-dimensional

system of Rydberg-dressed ultra-cold fermions within the G0W approximation. We use the static structure factor data from the Fermi-hypernetted-chain approximation to calculate

the screened interaction (i.e., the many-body local field factors), and then the Kukkonene-Overhauser effective interaction. At strong interaction strengths and intermediate

soft-core radius, we observe deeps and jumps in the real and imaginary parts of the self-energy, respectively. This behavior is related to the inelastic scattering of quasiparticles from the collective density modes. The quasiparticle lifetime diverges at the Fermi surface, and its wave-vector dependence deviates from the standard Landau Fermi liquid’s prediction,

i.e., |k−k_F |^{−2} for large soft-core radius and strong interactions, where the homogeneous system is close to the density-wave instability, i.e., droplet crystallization.

In the homogeneous liquid phase, the renormalization constant is suppressed by increasing either the interaction strength or soft-core radius. The many-body effective

mass is also reduced compared to its non-interacting values but its dependence on the coupling strength and soft-core radius is not monotonic. Signatures of approaching

the droplet crystal phase are observed in both the renormalization constant and effective mass. In the single-particle spectral function, two additional heavy modes emerge

at strong couplings. These composite excitations are undamped at small wave vectors. Due to the repulsion between the quasiparticle and composite excitations, we observe a

gap-like feature between the quasiparticle and composite excitation bands. The dispersions of composite modes merge at large wave vectors but remain well separated from the

single-particle excitation.