$p$-Wave Interactions in Low-Dimensional Fermionic Gases

We study a spin-polarized degenerate Fermi gas interacting via a $p$-wave Feshbach resonance in an optical lattice. The strong confinement available in this system allows us to realize one- and two-dimensional gases and, therefore, to restrict the asymptotic scattering states of atomic collisions. When aligning the atomic spins along (or perpendicular to) the axis of motion in a one-dimensional gas, scattering into channels with the projection of the angular momentum of $|m|=1$ (or $m=0$) can be inhibited. In two and three dimensions, we observe the doublet structure of the $p$-wave Feshbach resonance. For both the one-dimensional and the two-dimensional gases, we find a shift of the position of the resonance with increasing confinement due to the change in collisional energy. In a three-dimensional optical lattice, the losses on the Feshbach resonance are completely suppressed.

Figure 1

Spin-alignment dependent interactions in 1D and 2D. In the two-dimensional configuration of (a), all projections of the angular momentum in the $p$-wave collision are allowed. (b) and (c) show a one-dimensional spin-polarized Fermi gas with the spins aligned orthogonal and parallel to the extension of the gas, respectively. In (b), only the $|m|=1$ projection of the $p$-wave contributes to the scattering, in (c) only the $m=0$ projection.

Figure 2

Loss measurements of the $p$-wave Feshbach resonance. (a) Atoms are held in a crossed-beam optical dipole trap. (b) Two-dimensional Fermi gas ($V_z=25E_r$). (c) One-dimensional Fermi gas with the motion confined orthogonal to the direction of the magnetic field ($V_z=V_x=25E_r$). (d) One-dimensional Fermi gas with the motion confined parallel to the direction of the magnetic field ($V_z=V_y=25E_r$). (e) Fermi gas in a three-dimensional optical lattice ($V_x=V_y=V_z=25E_r$). The solid lines are Lorentzian fits to the data from which we extract the position and the width of the resonance.

Figure 3

(a) Shift of the Feshbach resonance position when tuning the gas from three to two dimensions. Open symbols indicate the position of the $m=0$ branch, solid symbols the $|m|=1$ branch of the resonance. The error bars denote the statistical error of 3 measurements. The solid lines show a calculation of the expected positions (see text). (b) Evolution of the full width at half maximum (FWHM) of the loss feature.

Figure 4

(a) Suppression of collisional losses in the $m=0$ partial wave versus the tunneling matrix element between the one-dimensional quantum gases. The bars reflect the errors determined from the fit to the loss peaks of two measurements. The gray box indicates the crossover region from a 2D to a 1D quantum gas as inferred from the inhibition of transverse collisions. (b) Shift of the position of the Feshbach resonance when tuning the gas from 2D to 1D. Open symbols indicate the position of the $m=0$ branch in the $y\mathrm{\text{−}}z$ lattice [see Fig. 1c] and the solid symbols the $|m|=1$ branch of the resonance in the $x\mathrm{\text{−}}z$ lattice [see Fig. 1b]. The solid lines show a calculation of the expected positions (see text). (c) Width of the Feshbach resonance loss feature.