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We study theoretically the deformation of the Fermi surface (FS) of athree-dimensional gas of Rydberg-dressed $^6$Li atoms. The laser dressing tohigh-lying Rydberg $D$ states results in angle-dependent soft-core-shapedinteractions whose anisotropy is described by multiple spherical harmonics. Weshow that this can drastically modify the shape of the FS and that itsdeformation depends on the interplay between the Fermi momentum $k_F$ and thereciprocal momentum $\bar{k}$ corresponding to the characteristic soft-coreradius of the dressing-induced potential. When $k_F< \bar{k}$, the dressedinteraction stretches a spherical FS into an ellipsoid. When $k_F\gtrsim\bar{k}$, complex deformations are encountered which exhibit multipolarcharacteristics. We analyze the formation of Cooper pairs around the deformedFS and show that they occupy large orbital angular momentum states ($p$, $f$,and $h$ wave) coherently. Our study demonstrates that Rydberg dressing to highangular momentum states may pave a route toward the investigation ofunconventional Fermi gases and multiwave superconductivity.

Multipolar Fermi-surface deformation in a Rydberg-dressed Fermi gas with long-range anisotropic interactions