Experimental determination of $p$-wave scattering parameters in ultracold ${}^6$Li atoms

We report the experimental determination of the scattering parameters for a $p$-wave Feshbach resonance in a single-component Fermi gas of ${}^6$Li atoms in the lowest spin state. The time scale of the cross-dimensional relaxation reflects the elastic-scattering rate of the atoms, and scattering parameters are determined from the scattering rate as a function of magnetic field by taking into account the momentum distribution and inhomogeneous density profile of the atoms in a trap. Precise determination of the scattering parameters for a $p$-wave Feshbach resonance is an important step toward the realization of a $p$-wave superfluid in an ultracold atomic gas.

Figure 1

Fraction of atoms remaining after 50-ms holding time near the $|1\rangle -|1\rangle$ $p$-wave Feshbach resonance as a function of magnetic-field strength. The atomic loss feature becomes broader at the higher magnetic-field side at higher temperature because of the wider spread of the momentum distribution. The sharp edge at the lower magnetic-field side of the atomic loss feature indicates the position of the Feshbach resonance.

Figure 2

Experimental time chart of the magnetic field. The magnetic field is swept quickly toward the lower-field side of the resonance ($B_{\mathrm{res}}$) to avoid adiabatic creation of $p$-wave molecules. Then, the trapping laser intensity is modulated for 3 ms with twice the trap frequency in one direction to add kinetic energy. The magnetic field is set close to the resonance ($B_{\mathrm{hold}}$) where the elastic collision rate is measured. After holding the atoms at $B_{\mathrm{hold}}$, the magnetic field is quickly swept to zero when atoms are released from the trap.

Figure 3

Time evolution of the anisotropy of the momentum distribution measured after a 4-ms TOF. (a) Momentum distribution measured before the parametric excitation. Atoms are seen to expand isotropically. (b) Momentum distribution measured just after the parametric excitation. The momentum distribution is wider in the vertical direction than in the horizontal direction in the image. (c) Momentum distribution after reaching thermal equilibrium due to interatomic scattering. Momentum distribution is observed to be isotropic again. (d) A typical time evolution of an aspect ratio as a function of hold time $T_{\mathrm{hold}}$.

Figure 4

Thermalization rate as a function of magnetic field measured near the $p$-wave Feshbach resonance for four different temperatures. Markers show the experimental data, and solid curves show the fitting result using Eq. (2). The zero of the magnetic-field detuning is determined from the loss measurement shown in Fig. 1.