Phase separation of atomic Bose-Fermi mixtures in an optical lattice

We study a two-dimensional atomic mixture of bosons and fermions cooled into their quantum degenerate states and subject to an optical lattice. The optical lattice provides van Hove singularities in the fermionic density of states. We find that these van Hove singularities produce new and interesting features for the transition towards phase separation: an arbitrary weak interaction between the bosons and the fermions is sufficient to drive the phase separation at low temperatures. The phase-separated state turns stable for attractive and repulsive interactions between the bosons and fermions and can be cast into the standard form of a “liquid–gas” transition.

Figure 1

$n_{\mathrm{F}}\text{−}T$ phase diagram. The grey region denotes the phase-separated regime, while the solid line denotes the line of fixed chemical potential ${\overline{\mu }}_{\mathrm{F}}$. The dotted lines describe fixed chemical potentials $\left({\mu }_{\mathrm{F}}-{\overline{\mu }}_{\mathrm{F}}\right)∕T_{\text{PS}}=\pm 0.02,0.06,0.01,0.14,0.18$. The lines derive from Eq. (28) with $\lambda =0.2$ and the dispersion relation (12).

Figure 2

Sketch of the fermionic and bosonic density profiles in the weak-coupling limit ${\lambda }_{\text{FB}}⪡1$. (a) The fermionic density exhibits a jump in the density by $2\delta {\overline{n}}_{\mathrm{F}}$ as the first-order transition line is crossed. At the same position in space, also the bosonic density exhibits a jump. For an attractive interaction $U_{\text{FB}}<0$ between the bosons and the fermions the bosonic density increases [see (b)], while for repulsive interaction $U_{\text{FB}}>0$ the bosonic density decreases at the jump (c).