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

We report the observation of a dimensional crossover of a narrow $p$-wave Feshbach resonance in an ultracold, spin-polarized $^6$Li Fermi gas confined by a one-dimensional optical lattice. In the three-dimensional limit, atom loss near the resonance has a larger contribution from the $|m_l|=1$ channel, reflecting its twofold orbital degeneracy in an isotropic system. As the lattice confinement is increased and the system approaches the quasi-two-dimensional regime, the relative contributions of the $|m_l|=1$ and $m_l=0$ channels evolve continuously, with an apparent suppression of the $|m_l|=1$ feature. By quantitatively analyzing both the orbital branching ratio and confinement-induced shift of the orbital splitting, we show that this evolution arises from an orbital-dependent modification of $p$-wave interactions induced by reduced dimensionality. Our results establish dimensional confinement as a powerful tool for controlling orbital degrees of freedom in resonantly interacting Fermi gases, and provide new insight into how reduced dimensionality reshapes anisotropic interactions in quantum matter.