We report the observation of a dimensional crossover of a $p$-wave Feshbach resonance in an ultracold, spin-polarized ${}^6\mathrm{Li}$ Fermi gas confined by a one-dimensional optical lattice. Using high-resolution atom-loss spectroscopy, we resolve the orbital doublet associated with the $m_{\ell }=0$ and $|m_{\ell }|=1$ scattering channels over a wide range of lattice depths. In the weak-confinement regime, the atom loss signal associated with the $|m_{\ell }|=1$ 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. These results provide an experimental characterization of orbital-dependent $p$-wave scattering in reduced dimensions and motivate future microscopic studies of confined anisotropic scattering.

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• Cold gases in optical lattices
• Fermi gases
• Scattering of atoms, molecules, clusters & ions
• Ultracold collisions