  We study two mobile bosonic impurities immersed in a one-dimensional optical
lattice and interacting with a bosonic bath. We employ the exact
diagonalization method for small periodic lattices to study stationary
properties and dynamics. We consider the branch of repulsive interactions that
induce the formation of bound impurities, akin to the bipolaron problem. A
comprehensive study of ground-state and low-energy properties is presented,
including an examination of the interaction strengths which induce the
formation of a bound dimer of impurities. We also study the dynamics induced
after an interaction quench to examine the stability of the bound dimers. We
reveal that after large interaction quenches from strong to weak interactions
the system can show large oscillations over time with revivals of the dimer
states. We find that the oscillations are driven by selected eigenstates with
phase-separated configurations.
