We study a highly imbalanced Fermi gas in a one-dimensional optical lattice from the polaronic point of view. The time-evolving block decimationg algorithm is used to calculate the ground state and dynamics of the system. We find qualitatively simila
r polaronic behaviour as in the recent experiment by Schirotzek et al. cite{Schirotzek2009a} where radio-frequency spectroscopy was used to observe polarons in three-dimensional space. In the weakly interacting limit our exact results are in excellent agreement with a polaron ansatz, and in the strongly interacting limit the results match with an approximative solution of the Bethe ansatz, suggesting a crossover from a quasiparticle to a charge-density excitation regime.
