Collisional Control of Ground State Polar Molecules and Universal Dipolar Scattering

We explore the impact of the short-range interaction on the scattering of ground state polar molecules and study the transition from a weak to strong dipolar scattering over an experimentally reasonable range of energies and electric field values. In the strong dipolar limit, the scattering scales with respect to a dimensionless quantity defined by mass, induced dipole moment, and collision energy. The scaling has implications for all quantum mechanical dipolar scattering. Furthermore the universal scattering regime will readily be achieved with polar molecules at ultracold temperatures.

Figure 1

(a) The variation of the cross section for many different electric fields with different short-range potentials. Different fields correspond to sets of colored curves; in ascending order the fields are 0.5 (black), 1 (red), 2 (blue), and 5 (brown) ${\mathcal{E}}_0$. (b) The average total cross section, $\overline{\sigma }$, (black) for various field values (in ascending order 0.5, 0.75, 1, 1.5, 2, 3, 4, and 5 ${\mathcal{E}}_0$) and the variations, $\Delta \sigma$, about $\overline{\sigma }$ (blue with circles). In both plots the red dashed line is ${\sigma }_Q$ and the green dash-dotted line is proportional to $E^{-1/2}$ as suggested by ${\sigma }_{\mathrm{SC}}$.

Figure 2

The transition of dipolar scattering to a universal behavior is shown by plotting $\mathcal{T}$ vs $\xi$ for many polar molecules. The molecules are ${}^{87}\mathrm{Rb}{}^{41}\mathrm{K}$ (black ×), fermionic ${}^{87}\mathrm{Rb}{}^{40}\mathrm{K}$ (black +), NaCs (brown □), and RbCs (red ⋄). The unitarity limit is 4, and is denoted by the dashed line. The blue line with triangles is proportional to $\xi$. The inset is the $\mathcal{T}$ obtained from the experimental cross section for Rydberg atoms from Ref. 21, and the blue line with open circles is the thermally averaged Eq. (7).