Density-Matrix Renormalization Group Study of Trapped Imbalanced Fermi Condensates

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.