Stability of resonantly interacting heavy-light Fermi mixtures

We investigate a two-component mixture of resonantly interacting Fermi gases as a function of the ratio $\kappa$ of the heavy to the light mass of the two species. The diffusion Monte Carlo method is used to calculate the ground-state energy and the pair correlation function starting from two different guiding wave functions, which describe, respectively, the superfluid and the normal state of the gas. Results show that the mixture is stable and superfluid for mass ratios smaller than the critical value ${\kappa }_c=13\pm 1$. For larger values of $\kappa$ simulations utilizing the wave function of the normal state are unstable towards cluster formation. The relevant cluster states driving the instability appear to be formed by one light particle and two or more heavy particles within distances on the order of the range of the interatomic potential. The small overlap between the wave function of the trimer bound state and the guiding wave function used to describe the superfluid state produces the unphysical stability of the superfluid gas above ${\kappa }_c$.

Figure 1

Energy per particle in units of ${\epsilon }_{\text{IFG}}$ as a function of the mass ratio $\kappa$. Diamonds correspond to the results for the superfluid state. Circles and squares correspond instead to simulations of the normal state with a number of walkers $N_w=1000$ and 5000, respectively. The insets show for this latter case a two-dimensional projected density for two different values of $\kappa$.

Figure 2

Energy per particle of the normal state with $N=14$ as a function of the inverse of the number of walkers $N_w$ for $\kappa =10$, 12, and 14 (respectively, red, green, and blue symbols). The inset shows the energy probability distribution for the same values of $\kappa$ and $N_w=800$.

Figure 3

Pure estimators for the two-body radial distribution functions $g_2^{hh}\left(r\right)$ and $g_2^{ll}\left(r\right)$ for two different values of $\kappa$. Distances are in units of the interaction range $R$ and in these units $k_F^{-1}\simeq 32$. The pair correlation function of an ideal Fermi gas is also shown for comparison.

Figure 4

Results for the integrated distribution function $g_2^{\text{int}}\left(R_c\right)$ defined in Eq. (6) as a function of the mass ratio $\kappa$ for the case of $ll$ and $hh$ particles. In both cases, $R_c=8R$.

Figure 5

Probability distribution as a function of the distances $|{\mathit{r}}_1^h-{\mathit{r}}^l|$ and $|{\mathit{r}}_2^h-{\mathit{r}}^l|$ for a three-particle system composed by two heavy and one light particles with mass ratio $\kappa =20$. (a) Normal wave function. (b) Superfluid wave function.