$s$-Wave Interaction in a Two-Species Fermi-Fermi Mixture at a Narrow Feshbach Resonance

We investigate $s$-wave interactions in a two-species Fermi-Fermi mixture of ${}^6\mathrm{Li}$ and ${}^{40}\mathrm{K}$. We develop for this case the method of cross-dimensional relaxation and find from a kinetic model, Monte Carlo simulations, and measurements that the individual relaxation rates differ due to the mass difference. The method is applied to measure the elastic cross section at the Feshbach resonance that we previously used for the production of heteronuclear molecules. Location ($B_0=155.09(5)\mathrm{G}$) and width are determined for this resonance. This reveals that molecules are being produced on the atomic side of the resonance within a range related to the Fermi energies, therefore establishing the first observation of a many body effect in the crossover regime of a narrow Feshbach resonance.

Figure 1

Comparison of kinetic model (solid curve) and classical Monte Carlo simulations with varying initial starting conditions (symbols): (a) triangles: $N_1=N_2$, $E_x/E_z=1.2$, $E_y/E_z=1.65$, (b) crosses: $N_1=N_2$, $E_x/E_z=1.7$, $E_y/E_z=1.4$, (c) plus symbols: $N_1=2N_2$, $E_x/E_z=1.6$, $E_y/E_z=1.3$.

Figure 2

Cross-dimensional thermal relaxation of ${}^6\mathrm{Li}$ and ${}^{40}\mathrm{K}$ in the mixture by interspecies elastic collisions at 152.8 G. The initial conditions for ${}^6\mathrm{Li}$ (${}^{40}\mathrm{K}$) are $N=3.5\times {10}^4$ ($8.0\times {10}^4$), $E_x/E_z=1.8$ (2.2) and $E_y/E_z=1.2$ (1.8). Uncertainty in the determination of atom numbers is assumed to be 50%.

Figure 3

Scattering cross sections measured with cross-dimensional thermal relaxation across an interspecies Feshbach resonance between ${}^6\mathrm{Li}$ and ${}^{40}\mathrm{K}$. The solid line is a guide to the eye and corresponds to an ab initio curve with the parameters $B_0=155.1\mathrm{G}$, $\Delta =0.81\mathrm{G}$, $a_{\mathrm{bg}}=63.5a_0$ [6], $k=k_F$, and ${\mu }_{\mathrm{rel}}=1.7{\mu }_B$ as obtained from a simple asymptotic bound state model calculation [6].