Trapping and Cooling Fermionic Atoms into Mott and Néel States

We perform a theoretical study of a fermionic gas with two hyperfine states confined to an optical lattice. We derive a generic state diagram as a function of interaction strength, particle number, and confining potential. We discuss the central density, the double occupancy, and their derivatives as probes for the Mott state, connecting our findings to the recent experiment of Jördens et al. [Nature (London) 455, 204 (2008)]. Using entropic arguments we compare two different strategies to reach the antiferromagnetic state in the presence of a trapping potential.

Figure 1

Left panel: State diagram for fermionic atoms as a function of interaction strength $u\equiv U/(6J)$ and scaled particle number $\rho \equiv N(V_t/6J{)}^{3/2}$. Symbols show results of DMFT calculations. The boundaries of the region (Mc) with a Mott insulator in the center of the trap are defined from the constraint $|n_0-1|<0.005$ on the central density. Lines are an analytical continuum approximation at $T=0$. Right panel: typical density profiles for regions (L), (Mc), and (Ms), with the radius $R$ set by $n(R)=0.1$.

Figure 2

First panel: Occupancy $n_0$ at the center of the trap and fraction $D$ of atoms residing on doubly occupied sites versus the scaled particle number $\rho$ at constant initial temperature $T_i/T_F=s/{\pi }^2=1.0/{\pi }^2$. The central occupancy $n_0$ and the “compressibilities” $\partial n_0/\partial \rho$ and $\partial D/\partial \rho$, for $u=5$, at two different initial temperatures $T_i/T_F=1.0/{\pi }^2$, $1.6/{\pi }^2$ are shown in the second and the third panel, respectively.

Figure 3

Upper panel: Central occupancy $n_0$ versus temperature for different interaction strengths. Lower panel: double occupancy $D$ versus temperature. ($\rho \approx 13.3$).

Figure 4

Entropy per particle $s$ of the total system (solid symbols) and the Mott region (open symbols) versus characteristic density $\rho$. The lowest $T$ is chosen slightly above the Néel temperature and the arrows delimit the density range where a central Mott plateau is formed.