Phase diagram of imbalanced strongly interacting fermions on a one-dimensional optical lattice

We show that the Hubbard Hamiltonian with particle-assisted tunneling rates—recently proposed to model a fermionic mixture near a broad Feshbach resonance—displays a ground-state phase diagram with superfluid, insulating, and phase-separated regimes. In the latter case, when the populations are balanced the two phases coexist in microscopic antiferromagnetic domains. Macroscopic phase segregation into a high-density superfluid of molecules and a low-density Fermi liquid of single atoms appears in the density profile above a critical polarization $p_c$.

Figure 1

(Color online) Number of pairs $n_d$ versus polarization $p$ at $\Delta =0$, and $\delta g=-t,\delta t=0.4t$ (continuous line, exact), $\delta g=-0.8t,\delta t=0$ (red diamonds, numerical). Inset: critical polarization $p_c$ vs filling $n$.

Figure 2

Exact phase diagram in the $\Delta \text{−}p$ plane at $n=0.9$, $\delta g=-t$, and $\delta t=0.4t$: the shaded region corresponds to macroscopic phase segregation in the density profile.

Figure 3

(Color online) Static charge structure factor $N\left(q\right)$ at different $p$ values, $L=N=16$, $\Delta =0$, $\delta t=0$, and $\delta g=-0.8t$ (figure), $\delta g=-0.6t$ (inset). In both cases, macroscopic phase separation emerges at $p\ge p_c$.