This study develops a novel experimental method of deducing the profile of interaction induced between impurities in a trapped gas of ultracold Fermi/Bose atoms, which are often referred to as Fermi/Bose polarons. In this method, we consider a two-body Fermi/Bose polaron collision experiment in which impurities and atoms interact only weakly. Numerical simulations of the quantum dynamics reveal the possibility to obtain information regarding the non-local induced interaction between two polarons from a measured profile of the polaron wave packet at several snapshots. This is because the potential of the induced interaction is well balanced by the quantum potential whenever the WKB approximation for the relevant Schr{o}dinger equation is applicable.
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