Luttinger Liquid of Trimers in Fermi Gases with Unequal Masses

We investigate one dimensional attractive Fermi gases in spin-dependent optical lattices. We show that three-body bound states--''trimers''--exist as soon as the two tunneling rates are different. We calculate the binding energy and the effective mass of a single trimer. We then show numerically that for finite and commensurate densities n↑=n↓/2 an energy gap appears, implying that the gas is a one-component Luttinger liquid of trimers with suppressed superfluid correlations. The boundaries of this novel phase are given. We discuss experimental situations to test our predictions.