Detecting the tunneling rates for strongly interacting fermions on optical lattices

Strongly interacting fermionic atoms on optical lattices are studied through a Hubbard-like model Hamiltonian, in which tunneling rates of atoms and molecules between neighboring sites are assumed to be different. In the limit of large on-site repulsion $U$, the model is shown to reproduce the $t$-$J$ Hamiltonian, in which the $J$ coefficient of the Heisenberg term depends on the particle-assisted tunneling rate $g$: explicitly, $J=4g^2/U$. At half-filling, $g$ drives a crossover from a Brinkman-Rice paramagnetic insulator of fully localized atoms ($g=0$) to the antiferromagnetic Mott insulator of the standard Hubbard case ($g=t$). This is observed already in the number of doubly occupied sites under the intermediate coupling regime, thus providing a criterion for extracting from measurements the effective value of $g$.

Figure 1

Processes between neighboring sites described by the three independent tunneling rates $t$, $g$, and $t_{\mathrm{ad}}$. Here slashed and filled circles represent single atoms (of arbitrary spin orientation) and diatomic molecules (doublons), respectively.

Figure 2

Ground-state energy density $e_{\mathrm{gs}}$ at half-filling, $t=1$, versus $U$ at three different $g$ values, as obtained by numerical simulations with DMRG on $L=80÷120$ sites. Dotted, dashed, and dot-dashed lines represent the results obtained for Hamiltonian (1), whereas solid lines are the results obtained for the Heisenberg model at the same parameter values. Asterisks denote in each case the value of $U$ ($U_{*}$) at which the two energies differ by less than $1\%$. Inset: $e_{\mathrm{gs}}$ versus $J$ at $t_{\mathrm{ad}}=0.8$ (diamonds), $t_{\mathrm{ad}}=0.4$ (squares), and $t_{\mathrm{ad}}=-0.8$ (triangles).

Figure 3

DMRG results for the number of doubly occupied sites (doublons) as a function of $g$ at different $t_{\mathrm{ad}}$ values, with $U=4t$. The solid horizontal lines represent the range of values of $g$ consistent with a given value of $n_d$. Dashed curves are guides for the eyes.