Breakdown of Universality for Unequal-Mass Fermi Gases with Infinite Scattering Length

We treat small trapped unequal-mass two-component Fermi gases at unitarity within a nonperturbative microscopic framework and investigate the system properties as functions of the mass ratio $\kappa$, and the numbers $N_1$ and $N_2$ of heavy and light fermions. While equal-mass Fermi gases with infinitely large interspecies $s$-wave scattering length $a_s$ are universal, we find that unequal-mass Fermi gases are, for sufficiently large $\kappa$ and in the regime where Efimov physics is absent, not universal. In particular, the $(N_1,N_2)=(2,1)$ and (3, 1) systems exhibit three-body and four-body resonances at $\kappa =12.314(2)$ and 10.4(2), respectively, as well as surprisingly large finite-range effects. These findings have profound implications for ongoing experimental efforts and quantum simulation proposals that utilize unequal-mass atomic Fermi gases.

Figure 1

(2, 1) system with $L^{\Pi }=1^{-}$ at unitarity. (a) Circles, crosses, and pluses show the SV energies, extrapolated to the ZR limit, for the three energetically lowest-lying states as a function of $\kappa$. Solid and dotted lines show $E_{f,0}$ ($q=0$ and 1) and $E_{g,0}$ ($q=-s_0$ and $-s_0+1$), respectively. (b) Pluses, squares, triangles, crosses, diamonds, and circles show the lowest SV energy for $\kappa =10$, 12, 12.3, 12.314, 12.4, and 12.5, respectively, as a function of $r_0$. Solid lines show fits to the SV energies. (c) Dotted and solid lines show $1/L_0(x_0)$ for $x_0=0.001$ as a function of $q$ for $s_0=1/2$ ($\kappa \approx 12.3131$) and $s_0=11/20$ ($\kappa \approx 12.0449$), respectively. The data for $s_0=11/20$ are scaled by a factor of 5 for enhanced readibility. In the ZR limit, the resonance condition implies $q=-1/2$, $1/2,\cdots$ for $s_0=1/2$ and $q=-11/20$, $9/20,\cdots$ for $s_0=11/20$ (see text for details).

Figure 2

Squares, triangles, and diamonds show the extrapolated ZR ground state energies of the (2, 2) system with $L^{\Pi }=0^{+}$, $1^{-}$, and $2^{+}$, respectively. The extrapolation to the ZR limit is based on 3–5 parameter fits to the SV energies for $r_0\approx 0.005a_{\mathrm{ho}}$ to $0.02a_{\mathrm{ho}}$. Circles and a solid line show the energies of the (2, 1) system with $L^{\Pi }=1^{-}$ [see Fig. 1a].