Instabilities in Binary Mixtures of One-Dimensional Quantum Degenerate Gases

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Abstract
We show that one-dimensional binary mixtures of bosons or of a boson and a spin-polarized fermion are Luttinger liquids with the following instabilities: (i) For different particle densities, strong attraction between the mixture components leads to collapse, while strong repulsion leads to demixing, and (ii) For a low-density mixture of two gases of impenetrable bosons (or a spin-polarized fermion and an impenetrable boson) of equal densities, the system develops a gap and exhibits enhanced pairing fluctuations when there is attraction between the components. In the boson-fermion mixture, the pairing fluctuations occur at finite momentum. Our conclusions apply to mixtures both on the continuum and on optical lattices away from integer or fractional commensurability.