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

Abstract

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.

Figures (4)

• Figure 1: Schematic of dimensional crossover and orbital anisotropy of $p$-wave interactions in a one-dimensional optical lattice. (a) Geometry of the lattice confinement. The magnetic field defines the quantization axis ($z$), while the lattice wave vector is along $x$. The $m_l=0$ (teal) and $|m_l|=1$ (blue) orbitals are indicated. Increasing lattice depth drives the system from a weakly modulated 3D geometry to an array of isolated quasi-2D pancake-shaped sites. (b) Evolution of the atom-loss spectrum across the dimensional crossover. Representative spectra are shown closed to the quasi-3D limit (left, $R = 1.94 \pm 0.25$), crossover region (middle, $R = 1.39 \pm 0.14$), and quasi-2D limit (right, $R = 1.08 \pm 0.10$). Gray circles represent the experimental data, with error bars (less than 4%) smaller than the circle size, solid black curves are total fits, and colored dashed lines indicate contributions from individual orbital branches.
• Figure 2: Branching ratio $R$ (a), temperature $T$ (b), resonance positions (c), and resonance splitting $\delta B$ which has a systemticaliy error with (d) versus lattice depth $s$, with solid lines indicating fits or model-based calculations, as described in the text. The horizontal dotted line in (d) indicates the experimentally measured 3D limit $\delta B_{\mathrm{3D}} = 7.8~\mathrm{mG}$Liu2026.
• Figure 3: Temperature dependence of the resonance splitting. (a) $T$ versus lattice depth $s$. (b) Resonance splitting $\delta B$ versus $s$, with a mean value of $8.92\,\mathrm{mG}$ (dashed line). (c) Splitting $\delta B$ versus $T_{\mathrm{tof}}$ at fixed lattice depths. The dashed lines indicate mean values of $8.07\,\mathrm{mG}$ for $s \approx 17$ and $9.17\,\mathrm{mG}$ for $s \approx 42$. Error bars and shaded regions represent the standard deviation.
• Figure 4: (a) Comparison of the measured time-of-flight temperature $T_{\mathrm{tof}}$ (blue circles) and the effective fit temperature $T_{\mathrm{eff}}$ (red circles) as a function of lattice depth $s$. While there is a systematic offset, both temperatures exhibit a consistent increasing trend with lattice depth. (b) The fitted product $A_i \times \kappa$ shows a monotonic decrease with increasing lattice depth $s$, reflecting a reduced effective loss strength in the deep-lattice regime.