Fermionic atoms in optical superlattices

Fermionic atoms in an optical superlattice can realize a very peculiar Anderson lattice model in which impurities interact with each other through a discretized set of delocalized levels. We show that under these finite-size features strongly correlated phases appear. By tuning the parameters of the superlattice two different phases could be observed: a Kondo-singlet phase in which each impurity forms a singlet with the Fermi level of its neighboring conducting islands, and a magnetic phase in which long range magnetic order is established between the impurities mediated by the intermediate islands. The interplay between these two phenomena depends on the parity of the number of particles per discretized set. We show how Kondo-induced resonances of measurable size can be observed through the atomic interference pattern.

Figure 1

(Color online) AHM for atoms in a superlattice (see text).

Figure 2

(Color online) Energy gain, $T$, as a function of $J∕t$. Different curves correspond to increasing values of $L(N=L∕2)$. For realistic cases (in orange), the arrows mark points at which $T=2\Delta$, to the right of which expression (4) is not valid.

Figure 3

(Color online) Spin-spin correlation functions of a fixed $f$-site $(s=5)$ with the rest of sites (a) and the $k$-momentum states of a neighboring island (b), as a function of $t∕J$. Parameters: $M=9$, $N=11(N_c=4)$, $U=0$, $U_f=10\Delta ϵ$, and $\Delta ϵ=10J$. In the inset of (a) correlations of supersite 5 with sites 6, 7, and supersite 9 are plotted.

Figure 4

(Color online) Same as in Fig. 3 with $N=9(N_c=3)$. The Kondo temperature is plotted in the inset of (b).

Figure 5

(Color online) Experimental scheme (see text). The renormalized parameters are $\widetilde{\Delta ϵ}={\omega }_{\mathrm{HF}}+\Delta ϵ-D$ (with ${\omega }_{\mathrm{HF}}$ the hyperfine frequency), and $\tilde{V}=\Omega V$.