This study develops an experimental method of deducing the profile of interaction induced between impurities in a trapped gas of ultracold Fermi or Bose atoms, which are often referred to as Fermi or Bose polarons. In this method, we consider a two-body Fermi or 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 nonlocal-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 Schrödinger equation is applicable.
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