Ground state of a Fermi gas with tilted dipoles

In the presence of an anisotropic and long-range dipole-dipole interaction, the Fermi sphere of an ultracold Fermi gas deforms into an ellipsoid. Recently, it was experimentally observed in such systems that the shape of the Fermi surface follows the rotation of the dipoles when they are tilted [1]. Here we generalize the Hartree-Fock mean-field theory of Refs.~[2, 3], where the dipoles were assumed to be parallel to one of the trap axes, to an arbitrary orientation of the dipoles and obtain the ground-state Thomas-Fermi radii and momenta. The calculated angular dependence of the Fermi surface deformation shows good agreement with experimental observations. We also find that the angular dependence of the aspect ratio turns out to be a direct consequence of the dipole tilting. \newline [1] K. Aikawa, et al., Science {\bf 345}, 1484 (2014).\newline [2] F. W\"{a}chtler, et al., Phys. Rev. A {\bf 96}, 043608 (2017).\newline [3] V. Velji\'{c}, et al., Phys. Rev. A {\bf 95}, 053635 (2017).