Quantitative determination of the hubbard model phase diagram from optical lattice experiments by two-parameter scaling

Precise shaping of laser light by an acousto-optic deflector

We present a laser beam shaping method using acousto-optic deflection of light and discuss its application to dipole trapping of ultracold atoms. By driving the acousto-optic deflector with multiple frequencies, we generate an array of overlapping diffraction-limited beams that combine to form an arbitrary-shaped smooth and continuous trapping potential. Confinement of atoms in a flat-bottomed potential formed by a laser beam with uniform intensity over its central region confers numerous advantages over the harmonic confinement intrinsic to Gaussian beam dipole traps and many other trapping schemes. We demonstrate the versatility of this beam shaping method by generating potentials with large flat-topped regions as well as intensity patterns that compensate for residual external potentials to create a uniform background to which the trapping potential of experimental interest can be added.

Exact exchange-correlation potential of an ionic Hubbard model with a free surface

In Kohn-Sham density functional theory (DFT) the interacting electron problem is mapped into a noninteracting problem in an effective potential v_KS. It is known that the charge gap of the interacting system is different from the gap of the effective problem due to a jump Δ_xc in v_KS when an electron is added but its magnitude and its role in the ubiquitous discrepancy between the experimental gaps and approximate DFT computations is poorly understood. Here we compute the exact v_KS of a strongly interacting one-dimensional lattice model which can be driven from an ionic to a Mott insulating state. Presence of a “vacuum” region allows to determine the absolute value of v_KS. We show that in the ionic regime Δ_xc is determined by nearest-neighbor interaction, while in the Mott regime Δ_xc is determined by on-site Hubbard interaction.

Discerning incompressible and compressible phases of cold atoms in optical lattices

Experiments with cold atoms trapped in optical lattices offer the potential to realize a variety of novel phases but suffer from severe spatial inhomogeneity that can obscure signatures of new phases of matter and phase boundaries. We use a high temperature series expansion to show that compressibility in the core of a trapped Fermi-Hubbard system is related to measurements of changes in double occupancy. This core compressibility filters out edge effects, offering a direct probe of compressibility independent of inhomogeneity. A comparison with experiments is made.