Stability and pairing in quasi-one-dimensional Bose-Fermi mixtures

We consider a mixture of single-component bosonic and fermionic atoms in an array of coupled one-dimensional "tubes". For an attractive Bose-Fermi interaction, we show that the system exhibits phase separation instead of the usual collapse. Moreover, above a critical inter-tube hopping, all first-order instabilities disappear in both attractive and repulsive mixtures. The possibility of suppressing instabilities in this system suggests a route towards the realization of paired phases, including a superfluid of p-wave pairs unique to the coupled-tube system, and quantum critical phenomena.