  The density-matrix renormalization group is employed to investigate a
harmonically-trapped imbalanced Fermi condensate based on a one-dimensional
attractive Hubbard model. The obtained density profile shows a flattened
population difference of spin-up and spin-down components at the center of the
trap, and exhibits phase separation between the condensate and unpaired
majority atoms for a certain range of the interaction and population imabalance
$P$. The two-particle density matrix reveals that the sign of the order
parameter changes periodically, demonstrating the realization of the
Fulde-Ferrell-Larkin-Ovchinnikov phase. The minority spin atoms contribute to
the quasi-condensate up to at least $P \simeq 0.8$. Possible experimental
situations to test our predictions are discussed.
