From Cooper Pairs to Luttinger Liquids with Bosonic Atoms in Optical Lattices

We propose a scheme to observe strongly correlated fermionic phenomena with bosonic atoms in optical lattices. For different values of the sign and strength of the scattering lengths, it is possible to reach either a “superconducting” regime, where the system exhibits atomic pairing, or a Luttinger liquid behavior. We identify the range of parameters where these phenomena appear, illustrate our predictions with numerical calculations, and show how to detect the presence of pairing.

Figure 1

Projection of the exact ground state onto the one corresponding to the limit $U\to \infty$ as a function of $|V|/U$ for $N=6$, $M=8$, and different values of $t/U$.

Figure 2

$|\phi {|}^2$ as a function of $\Delta /U$ for the variational wave function (5) and for $N=6$, $t=0.1U$, and different values of $|V|/U$.

Figure 3

Gap for spin excitations, $\delta /U$, as a function of $|V|/U$ for $N=6$, and $t=0.1U$. The three regimes are indicated in the figure.

Figure 4

$⟨S_z^2⟩$ as a function of $B/U$, for $N=6$, $t=0.1U$, and different values of $V/U$. The inset shows the second derivative, $\eta$, of $⟨S_z^2⟩$ with respect to $B$ (in units of $U$) at zero magnetic field, as a function of $|V|/U$.