  We show that the two-band nature of noncentrosymmetric superconductors leads
naturally to an anomalous Josephson current appearing at zero phase difference
in a clean noncentrosymmetric superconductor/ferromagnet/noncentrosymmetric
superconductor junction. The two-band nature provides two sets of Andreev bound
states which carry two supercurrents with different amplitudes. When the
magnetization direction of the ferromagnet is suitably chosen, two
supercurrents experience opposite phase shifts from the conventional sinusoidal
current-phase relation. Then the total Josephson current results in a
continuously tunable ground-state phase difference by adjusting the ferromagnet
parameters and the triplet-singlet ratio of noncentrosymmetric superconductors.
The physics picture and analytical results are given on the basis of the
$s$+$p$ wave, while the numerical results are reported on both $s$+$p$ and
$d$+$p$ waves. For the $d$+$p$ wave, we find novel states in which the
supercurrents are totally carried by continuous propagating states instead of
discrete Andreev bound states. Instead of carrying supercurrent, the Andreev
bound states which here only appear above the Fermi energy block the
supercurrent flowing along the opposite direction. These novel states advance
the understaning of the relation between Andreev bound states and the Josephson
current. And the ground-state phase difference serves as a tool to determine
the triplet-singlet ratio of noncentrosymmetric superconductors.
