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 intertube 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.

Figure 1

Zero temperature, mean-field phase diagrams in density space for a repulsive BF mixture with dimensionless hopping strength $t^{\prime }\equiv 2m_{f}t/c_f^2=0.5$ (left panel), and an attractive mixture with $t^{\prime }=0.2$ (right). Each mixture can either form a uniform BEC phase (light gray shaded region) or it can undergo a first-order transition (thick red lines) to a phase-separated state (dark gray). The dotted lines connect points on the first-order boundary with the same chemical potential. Filled circles mark stable tricritical points, where 1st and 2nd ($n_b=0$) order transition lines merge, while the empty circles correspond to unstable ones. Spinodal lines (blue dashed) divide the phase-separated region into the unstable domain (internal region) and the metastable domain (external). Note that, for the repulsive mixture, the phase at very low fermionic densities is always uniform.

Figure 2

Evolution of the stable (filled blue circles) and unstable (empty circles) tricritical points $n_f^{\mathrm{tcp}}/c_f$ ($n_b^{\mathrm{tcp}}=0$) as a function of the hopping strength $t^{\prime }$ for a repulsive mixture. For attractive mixtures, the tricritical points have the same values, but the stable and unstable branches are switched. The (dashed) line approximately separating the 1D from the 3D regime is $n_f/c_f=\sqrt{2t^{\prime }}\alpha /\pi$, with $\alpha \simeq 1.35$—this defines the point, ${\mu }_f-U_{\mathrm{BF}}{\Phi }^2=8t$, where the Fermi surface first touches the $xy$ band edge. Tricritical points disappear altogether above the critical value $t_{\mathrm{cr}}^{\prime }\simeq 1.19$.