Quantum simulation of a triatomic chemical reaction with ultracold atoms on a waveguide

We study the scaling and coordinate transformation to physically simulate quantum three-body collinear chemical reactions of the type A+BC $rightarrow$ AB+C by the motion of single ultracold atoms or a weakly interacting Bose-Einstein condensate on an $L$-shaped waveguide. As an example we show that the parameters to model the reaction F+HH $to$ H+HF with lithium are at reach with current technology. This mapping provides also an inverse scattering tool to find an unknown potential, and a way to transfer the knowledge on molecular reaction dynamics to design beam splitters for cold atoms with control of the channel outcome and vibrational excitation.