Measuring spin correlations in optical lattices using superlattice potentials

We suggest two experimental methods for probing both short- and long-range spin correlations of atoms in optical lattices using superlattice potentials. The first method involves an adiabatic doubling of the periodicity of the underlying lattice to probe neighboring singlet (triplet) correlations for fermions (bosons) by the occupation of the resulting vibrational ground state. The second method utilizes a time-dependent superlattice potential to generate spin-dependent transport by any number of prescribed lattice sites, and probes correlations by the resulting number of doubly occupied sites. For experimentally relevant parameters, we demonstrate how both methods yield large signatures of antiferromagnetic correlations of strongly repulsive fermionic atoms in a single shot of the experiment. Lastly, we show how this method may also be applied to probe $d$-wave pairing, a possible ground-state candidate for the doped repulsive Hubbard model.

Figure 1

(a) Adiabatically doubling the lattice wavelength forces the singlet (triplet) to enter the ground state for fermions (bosons). (b) Singlet probability for nearest-neighbors vs $T$ for the isotropic Heisenberg model. (c)–(e) A moving superlattice induces Landau-Zener transitions between neighboring lattice sites for spin-up atoms which have been transferred to the first excited states where the tunneling is higher than in the ground state. Atoms on even (odd) sites move right (left) following the superlattice minima (maxima).

Figure 2

(a) Probability distribution $|W_i{|}^2$ of the first vibrational excitation at even sites for moves $m=1,...,8$. The curves are offset for clarity. The inset confirms that the vibrational ground states remains stationary. (b) Probability distribution of the first excited states on odd sites. The inset shows the error probability for the three states in (a) and (b).

Figure 3

Average probability $\langle P_d\left(i\right)\rangle$ for a site to be doubly occupied vs $T$ after moves $m=1,...,8$ for the isotropic (a) 1D, (b) 2D, and (c) 3D Heisenberg model. (d) Same as (c) with the addition of a small exchange anisotropy $H_z=0.01J{\sum }_{\langle l,m\rangle }{\widehat{s}}_l^z{\widehat{s}}_m^z$.