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We propose a novel experimental method to extend the investigation ofion-atom collisions from the so far studied cold, essentially classical regimeto the ultracold, quantum regime. Key aspect of this method is the use ofRydberg molecules to initialize the ultracold ion-atom scattering event. Weexemplify the proposed method with the lithium ion-atom system, for which wepresent simulations of how the initial Rydberg molecule wavefunction, freed byphotoionization, evolves in the presence of the ion-atom scattering potential.We predict bounds for the ion-atom scattering length from ab initiocalculations of the interaction potential. We demonstrate that, in thepredicted bounds, the scattering length can be experimentally determined fromthe velocity of the scattered wavepacket in the case of$^\textsf{6}\textsf{Li}^\textsf{+}$ - $^\textsf{6}\textsf{Li}$, and from themolecular ion fraction in the case of $^\textsf{7}\textsf{Li}^\textsf{+}$ -$^\textsf{7}\textsf{Li}$. The proposed method to utilize Rydberg molecules forultracold ion-atom scattering, here particularized for the lithium ion-atomsystem, is readily applicable to other ion-atom systems as well.

Rydberg molecules for ion-atom scattering in the ultracold regime