  We study a model of one-dimensional fermionic atoms that can bind in pairs to
form bosonic molecules. We show that at low energy, a coherence develops
between the molecule and fermion Luttinger liquids. At the same time, a gap
opens in the spin excitation spectrum. The coherence implies that the order
parameters for the molecular Bose-Einstein Condensation and the atomic BCS
pairing become identical. Moreover, both bosonic and fermionic charge density
wave correlations decay exponentially, in contrast with a usual Luttinger
liquid. We exhibit a Luther-Emery point where the systems can be described in
terms of noninteracting pseudofermions. At this point, we provide closed form
expressions for the density-density response functions.
