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We investigate the ground state properties and the nonequilibrium dynamics ofa lattice trapped bosonic mixture consisting of an impurity species and afinite-sized medium. For the case of one as well as two impurities we observethat, depending on the lattice depth and the interspecies interaction strength,a transition from a strongly delocalized to a localized impurity distributionoccurs. In the latter regime the two species phase separate, thereby forming aparticle-hole pair. For two impurities we find that below a critical latticedepth they are delocalized among two neighboring outer lattice wells and aretwo-body correlated. This transition is characterized by a crossover fromstrong to a suppressed interspecies entanglement for increasing impurity-mediumrepulsion. Turning to the dynamical response of the mixture, upon quenching theinterspecies repulsion to smaller values, we reveal that the predominanttunneling process for a single impurity corresponds to that of a particle-holepair, whose dynamical stability depends strongly on the quench amplitude.During the time-evolution a significant increase of the interspeciesentanglement is observed, caused by the build-up of a superposition of statesand thus possesses a many-body nature. In the case of two bosonic impuritiesthe particle-hole pair process becomes unstable in the course of the dynamicswith the impurities aggregating in adjacent lattice sites while being stronglycorrelated.

Doping a lattice-trapped bosonic species with impurities: From ground state properties to correlated tunneling dynamics