Giant Cross Section for Molecular Ion Formation in Ultracold Rydberg Gases

We have studied the associative ionization of a Rydberg atom and a ground-state atom in an ultracold Rydberg gas. The measured scattering cross section is 3 orders of magnitude larger than the geometrical size of the produced molecule. This giant enhancement of the reaction kinetics is due to an efficient directed mass transport which is accelerated by the Rydberg electron. We also find that the total inelastic scattering cross section is given by the geometrical size of the Rydberg electron’s wave function.

Figure 1

Time of flight spectrum for the $30P_{3/2}$ state at a peak density of $n_0=3\times {10}^{13}{\mathrm{cm}}^{-3}$ showing the ${\mathrm{Rb}}^{+}$ and ${{\mathrm{Rb}}_2}^{+}$ peaks. The acquisition is started ($t=0$) when the excitation pulse is applied. After subtracting the fitted decay of the ${\mathrm{Rb}}^{+}$ peak, the signal of the molecular ions alone is obtained (inset).

Figure 2

(a) The slope of the linear dependency between the decay rate ${\gamma }_{\text{coll}}^0$ of the ${{\mathrm{Rb}}_2}^{+}$ peak and the atom flux $\mathrm{\Phi }$ through the Rydberg atom reveals the total inelastic scattering cross section ${\sigma }_{\text{inel}}$ between a Rydberg and a ground-state atom. (b) The scaling of the peak ratio $R_{\mathrm{AI}}/R_{\mathrm{PI}}$ reveals the partial scattering cross section for the creation of molecular ions ${\sigma }_{\mathrm{AI}}$.

Figure 3

Scaling of the measured scattering properties with the effective principal quantum number $n_{\mathrm{eff}}$. (a) The cross section for associative ionization ${\sigma }_{\mathrm{AI}}$ (red diamonds) exceeds the geometrical cross section of the formed ${{\mathrm{Rb}}_2}^{+}$ molecules (orange dashed line) by 3 orders of magnitude. The total inelastic scattering cross section ${\sigma }_{\text{inel}}$ (blue dots) is in very good agreement with the geometrical cross section of the Rydberg atom (solid green line). (b) The characteristic scattering radius (blue dots) coincides with the size of the Rydberg atom (green line). Langevin capture through polarization of the ground-state atom by the screened Rydberg core (purple line) is not sufficient to explain the observed scattering radii.

Figure 4

(a) Potential for the ground-state atom created by the interaction with the Rydberg core alone (green) and in combination with the Rydberg electron (blue). The potential is calculated in perturbation theory for triplet scattering. (b) Comparison of the $51P_{3/2}$ electronic wave function with the size of the formed ${{\mathrm{Rb}}_2}^{+}$ molecule. (c) Catalytic cycle enabled by the presence of the Rydberg electron. The solid line illustrates the quasicatalytic effect of the electron observed in our experiments. The electron of the Rydberg atom ${\mathrm{Rb}}^{*}$ vastly increases the probability of an inelastic collision with a ground-state atom Rb, ultimately leading to a metastable excited ${{\mathrm{Rb}}_2}^{*}$ molecule that subsequently ionizes into ${{\mathrm{Rb}}_2}^{+}$ through the dipole resonant mechanism [3]. In an ultracold plasma the recombination of ${\mathrm{Rb}}^{+}$ and $e^{-}$ into Rydberg states (dashed line) could complete the catalytic cycle.