Novel Superfluidity in a Trapped Gas of Fermi Atoms with Repulsive Interaction Loaded on an Optical Lattice

We investigate a possibility of superfluidity in a trapped gas of Fermi atoms with a repulsive interaction in the presence of an optical lattice. Applying the exact diagonalization method to a one-dimensional Hubbard model including the trap potential, we find that, when the strength of the repulsive interaction exceeds a critical value, the binding energy of two Fermi atoms becomes negative below the half-filling case, indicating that an attractive interaction effectively works between Fermi atoms. In this case, a “Mott insulating core” appears in the center of the trap, where each site is occupied by one atom. The Cooper-pair correlation strongly develops between atoms in the left- and right-hand sides of this core.

Figure 1

The binding energy $E_b$ as a function of the repulsive interaction $U/t$. $E_b$ is normalized by $t$. The number of Fermi atoms $N_F(n_{\uparrow },n_{\downarrow })$ equals (a) $10(5\uparrow ,5\downarrow )$, (b) $14(7\uparrow ,7\downarrow )$, and (c) $18(9\uparrow ,9\downarrow )$. The number of sites $N$ is 14. The strength of the trap potential $V/t$ varies from 1.5 to 9.5. In panel (a), the negative binding energy around $0.00>E_b>-0.06$ is magnified in the inset.

Figure 2

Density profile [$n(i)$] below the half filling (a) and at just the half filling (c) in $V/t=9.5$. Each of $n(i)$ displayed in panels (a) and (c) is measured at $U/t$ giving the binding energy $E_g$ marked in panels (b) and (d) ($E_b$ versus $U/t$), respectively. Note that the colors of the lines in panels (a) and (c) correspond to those of the marked circles in (b) and (d), respectively.

Figure 3

Density profile before and after adding two atoms (black and red lines, respectively) below the half-filling case in $V/t=9.5$. (a) $E_g>0(U/t=5.0)$. (b) $E_g<0(U/t=8.0)$. For $E_b$ versus $U/t$ in this case, see Fig. 2b.

Figure 4

Local site dependences of the singlet Cooper-pair correlation. We take $10(5\uparrow ,5\downarrow )$ and $V/t=9.5$. We find a strong pair correlation between $i=2$ and $j=13$ in the case of $U/t\ge 8.0$, where $E_b$ takes a negative sign. On the other hand, the local pair correlation between $i=7$ and other sites shows almost zero.