  We study an atomic Bose gas with an s-wave Feshbach resonance in a
one-dimensional optical lattice, with the densities of atoms and molecules
incommensurate with the lattice. At zero temperature, most of the parameter
region is occupied by a phase in which the superfluid fluctuations of atoms and
molecules are the predominant ones, due to the phase fluctuations of atoms and
molecules being locked by a Josephson coupling between them. When the density
difference between atoms and molecules is commensurate with the lattice, two
additional phases may exist: the two component Luttinger liquid where both the
atomic and molecular sectors are gapless, and the inter-channel charge density
wave where the relative density fluctuations between atoms and molecules are
frozen at low energy.
