We consider the effects of single impurities on polarons in three-dimensions (3D) using a continuous time quantum Monte-Carlo algorithm. An exact treatment of the phonon degrees of freedom leads to a very efficient algorithm and we are able to compute the polaron dynamics on an infinite lattice using an auxiliary weighting scheme. The magnitude of the impurity potential, the electron-phonon coupling and the phonon frequency are varied. We determine the magnitude of the impurity potential required for polaron trapping. For small electron-phonon coupling the number of phonons increases dramatically on trapping. The polaron binding diagram is computed, showing that intermediate-coupling low-phonon-frequency polarons are localized by exceptionally small impurities.
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