  We explore the ground states in population-imbalanced attractive 1-D
fermionic optical lattice filling $p$ orbitals over the lowest $s$ one by using
the density-matrix-renormalization-group (DMRG) method. The DMRG calculations
find the occurrence of spatially non-uniform off-diagonal long-range order. In
contrast to Fulde-Ferrel Larkin-Ovchinikov pair as observed in the single-band
Hubbard model. The spatial oscillation period of the pair correlation function
is widely fixed to be $\pi$ irrespective of the mismatch between spin-split
Fermi surfaces. The ground-state $\pi$ order corresponds to $\eta$-pair
condensate predicted by Yang [Phys. Rev. Lett. \textbf{63}, 2144 (1989)].
Taking account of the effects of harmonic traps, we confirm that the
$\eta$-pair state distinctly emerges at the center of the trap potential
surrounded by perfectly-polarized states even in the trapped cases.
