Universal relations and normal-state properties of a Fermi gas with laser-dressed mixed-partial-wave interactions

In a recent experiment [P. Peng, $et$ $al.$, Phys. Rev. A \textbf{97}, 012702 (2018)], it has been shown that the $p$-wave Feshbach resonance can be shifted toward the $s$-wave Feshbach resonance by a laser field. Based on this experiment, we study the universal relations and the normal-state properties in an ultracold Fermi gas with coexisting $s$- and $p$-wave interactions under optical control of a $p$-wave magnetic Feshbach resonance. Within the operator-product expansion, we derive the high-momentum tail of various observable quantities in terms of contacts. We find that the high-momentum tail becomes anisotropic. Adopting the quantum virial expansion, we calculate the normal-state contacts with and without a laser field for $^{40}$K atoms using typical experimental parameters. We show that the contacts are dependent on the laser dressing. We also reveal the interplay of laser dressing and different partial-wave interactions on various contacts. In particular, we demonstrate that the impact of the laser dressing in the $p$-wave channel can be probed by measuring the $s$-wave contacts, which is a direct manifestation of few-body effects on the many-body level. Our results can be readily checked experimentally.