Orbital-Dependent Dimensional Crossover of a $p$-Wave Feshbach Resonance

We report the observation of a dimensional crossover of a $p$-wave Feshbach resonance in an ultracold, spin-polarized ${}^6$Li Fermi gas confined by a one-dimensional optical lattice. Using high-resolution atom-loss spectroscopy, we resolve the orbital doublet associated with the $m_l=0$ and $\mathrm{\mid }{m}_l\mathrm{\mid }=1$ scattering channels over a wide range of lattice depths. In the weak-confinement regime, the atom loss signal associated with the $\mathrm{\mid }{m}_l\mathrm{\mid }=1$ branch is stronger, consistent with the twofold orbital degeneracy of the three-dimensional system. As the lattice confinement increases, the relative loss weight of the two orbital branches evolves continuously toward the quasi-two-dimensional limit, indicating a progressive suppression of relative motion along the lattice direction. In addition, we observe a systematic confinement dependence of the orbital splitting between the two resonance branches. Together, these observations are consistent with confinement-induced modifications of orbital-dependent $p$-wave scattering across the dimensional crossover. These results provide an experimental characterization of orbital-dependent $p$-wave scattering in reduced dimensions and motivate future microscopic studies of confined anisotropic scattering.