Heavy-Light Fermion Mixtures at Unitarity

We investigate fermion pairing in the unitary regime for a mass ratio corresponding to a ${}^6\mathrm{Li}\mathrm{\text{−}}{}^{40}\mathrm{K}$ mixture using quantum Monte Carlo methods. The ground-state energy and the average light- and heavy-particle excitation spectrum for the unpolarized superfluid state are nearly independent of the mass ratio. In the majority light system, the polarized superfluid is close to the energy of a phase separated mixture of nearly fully polarized normal and unpolarized superfluid. For a majority of heavy particles, we find an energy minimum for a normal state with a ratio of $\sim 3:1$ heavy to light particles. A slight increase in attraction to $k_{F}a\approx 2.5$ yields a ground state energy of nearly zero for this ratio. A cold unpolarized system in a harmonic trap at unitarity should phase separate into three regions, with a shell of unpolarized superfluid in the middle.

Figure 1

Quasiparticle excitation energies for the two different species. The QMC results are shown as diamonds and squares for light and heavy particles, respectively. The BCS results are shown as lines: the dashed line corresponds to light particles, the dot-dashed line to heavy particles, while the solid line to the results for the equal-mass case. Also shown are the QMC results (circles) from Ref. 8 for the equal-mass case, as well as the average (triangles) of the two QMC sets of points for heavy and light particles.

Figure 2

Equation of state of a heavy-light fermion mixture as a function of the polarization at constant density. Shown are results for the normal state (circles) as well as for the superfluid state (squares). The solid line is a polynomial best fit to the QMC results for the normal state.

Figure 3

Equation of state as a function of the concentration $x^{\prime }$ (left-hand panel) and $x$ (right-hand panel). Normal (circles) and superfluid states (squares) are shown. The dashed lines are the coexistence lines between the normal and the unpolarized superfluid states. The resulting critical concentrations are $x_c^{\prime }=0.02$ and $x_c=0.49$. The dotted curves represent noninteracting impurities with the calculated binding energies and effective masses.

Figure 4

The polarization of a trapped system as a function of the radius (scaled so that at $r_{\mathrm{sc}}=1$ the density goes to 0). Shown are curves for four different values of $P_{\mathrm{tot}}=(N_h-N_l)/(N_h+N_l)$.