  We study a balanced two-component system of ultracold fermions in one
dimension with attractive interactions and subject to a spin-dependent optical
lattice potential of opposite sign for the two components. We find states with
different types of modulated pairing order parameters which are conceptually
similar to pi-phases discussed for superconductor-ferromagnet heterostructures.
Increasing the lattice depth induces sharp transitions between states of
different parity. While the origin of the order parameter oscillations is
similar to the FFLO phase for paired states with spin imbalance, the current
system is intrinsically stable to phase separation. We discuss experimental
requirements for creating and probing these novel phases.
