Magnetic Control of the Interaction in Ultracold K-Rb Mixtures

We predict the presence of several magnetic Feshbach resonances in selected Zeeman sublevels of the isotopic pairs ${}^{40}\mathrm{K}\mathrm{\text{−}}{}^{87}\mathrm{R}\mathrm{b}$ and ${}^{41}\mathrm{K}\mathrm{\text{−}}{}^{87}\mathrm{R}\mathrm{b}$ at magnetic fields up to ${10}^3\mathrm{G}$. Positions and widths are determined combining a new measurement of the ${}^{40}\mathrm{K}\mathrm{\text{−}}{}^{87}\mathrm{R}\mathrm{b}$ inelastic cross section with recent experimental results on both isotopes. The possibility of driving a K-Rb mixture from the weak to the strong interacting regime tuning the applied field should allow one to achieve the optimal conditions for boson-induced Cooper pairing in a multicomponent ${}^{40}\mathrm{K}\mathrm{\text{−}}{}^{87}\mathrm{R}\mathrm{b}$ atomic gas and for the production of ultracold polar molecules.

Figure 1

The numerically calculated inelastic rate $G^{\mathrm{i}\mathrm{n}\mathrm{e}\mathrm{l}}$ for ${}^{40}\mathrm{K}(9/2,9/2)+{}^{87}\mathrm{R}\mathrm{b}(2,1)$ collisions at temperature $T=500\mathrm{n}\mathrm{K}$ as a function of the singlet “scattering phase” (see text) for $a_t=-330a_0$ (full line) and $a_t=-490a_0$ (dashed line). The horizontal lines correspond to the bounds determined experimentally.

Figure 2

Field dependence of the ${}^{40}\mathrm{K}(9/2,-9/2)+{}^{87}\mathrm{R}\mathrm{b}(1,1)$ (full line) and ${}^{40}\mathrm{K}(9/2,-7/2)+{}^{87}\mathrm{R}\mathrm{b}(1,1)$ (dashed line) scattering lengths for $a_s=-105a_0$, $a_t=-380a_0$, and the nominal $C_6$. The arrow shows the best working point for inducing the Cooper pairing instability (see text).

Figure 3

Field dependence of the purely real $a_{11,11}$ and of the real part $\mathcal{R}{a}_{1-1,1-1}$ for ${}^{41}\mathrm{K}\mathrm{\text{−}}{}^{87}\mathrm{R}\mathrm{b}$ collisions and the nominal $a_s$, $a_t$, $C_6$. Approximate zero-field quantum numbers $f$, with $\overrightarrow{f}={\overrightarrow{f}}_a+{\overrightarrow{f}}_b$, are assigned to the resonances. Near the $(2,-2)+(1,0)$ channel threshold $B_t$ (vertical line) $\mathcal{R}{a}_{1-1,1-1}$ changes dramatically.