Universal resonant ultracold molecular scattering

The elastic scattering amplitudes of indistinguishable, bosonic, strongly polar molecules possess universal properties at the coldest temperatures due to wave propagation in the long-range dipole-dipole field. Universal scattering cross sections and anisotropic threshold angular distributions, independent of molecular species, result from careful tuning of the dipole moment with an applied electric field. Three distinct families of threshold resonances also occur for specific field strengths, and can be both qualitatively and quantitatively predicted using elementary adiabatic and semiclassical techniques. The temperatures and densities of heteronuclear molecular gases required to observe these universal characteristics are predicted.

Figure 1

(Color online) Adiabatic potential curves for bosonic polar molecules. The curves are labeled by their asymptotic angular momentum $\ell$ and by the magnitude of the conserved magnetic quantum number $m$.

Figure 2

(Color online) Channel contributions to the threshold cross section for $r_0=0.0111$ dipole units. The (0,0) and degenerate (2,1) channels dominate scattering below $\sim 14E_D$.

Figure 3

(Color online) Near-threshold cross section as a function of the cutoff radius. Positions of the (2,0) Feshbach-shape resonances are marked by $\times \mathrm{s}$ and labeled as $R1$, $R2$, $R3$, $R4$.

Figure 4

(Color online) Cross-section dependence on the angle between the incident direction and the field axis, for values of the cutoff radius $r_0$ (in dipole units) in the vicinity of the Feshbach/shape resonance. When the total cross section is large, the scattering is almost isotropic, even at the “$d$-wave” resonance, (c).

Figure 5

(Color online) Electric field dependence of the near-threshold LiF elastic scattering cross section, in both (a) absolute and (b) dipole units. The minima of the cross section $(=2D^2)$ in the upper figure rise rapidly with the field as a result of rapidly growing dipole length.