  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 similar 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.
