Analytic expressions for Hubbard models with arbitrary structures in programmable optical lattices

We investigate the use of programmable optical lattices for quantum simulation of Hubbard models, determining analytic expressions for the hopping and Hubbard U, finding that they are suitable for emulating strongly correlated systems with arbitrary structures, including those with a multiple site basis and impurities. Programmable potentials are highly flexible, with the ability to control the depth and shape of individual sites in the optical lattice dynamically. Quantum simulators of Hubbard models with (1) an arbitrary basis are required to represent many real materials of contemporary interest, (2) broken translational symmetry are needed to study impurity physics, and (3) dynamical lattices are needed to investigate strong correlations out of equilibrium. We derive analytic expressions for Hubbard Hamiltonians in programmable potential systems. We find experimental parameters for quantum simulation of Hubbard models with an arbitrary basis, concluding that programmable optical lattices are suitable for this purpose. Finally, we demonstrate how programmable optical lattices can be used for quantum simulation of ionic Hubbard models, and thus the onset of charge transfer insulating states, in parameter regimes that are currently inaccessible to experiment.

Automated summary

This study explores the use of programmable optical lattices for quantum simulation of Hubbard models, finding that they are flexible for emulating complex systems and studying strong correlations and impurity effects. The results indicate that programmable optical lattices show great potential in simulating Hubbard models with arbitrary structures and characteristics.