Localization of an impurity particle on a boson Mott insulator background

We investigate the behavior of a single particle hopping on a three dimensional cubic optical lattice in the presence of a Mott insulator of bosons in the same lattice. We calculate the critical interaction strength between the impurity and background bosons, beyond which there is bound state (polaron) formation. We give exact results in the limit of a perfect Mott insulator, where polaron formation is equivalent to impurity localization. We calculate the effects of lattice anisotropy, higher impurity bands, and fluctuations of the Mott insulator on the localization threshold. We argue that our results can be checked experimentally by RF spectroscopy of impurity particles.