Hubbard models with arbitrary structures in programmable optical lattices

TL;DR

This paper demonstrates that programmable optical lattices can be used to simulate complex Hubbard models with arbitrary structures, including impurities and dynamical properties, by deriving analytic expressions and identifying suitable experimental parameters.

Contribution

It provides analytic formulas for Hubbard Hamiltonians in programmable lattices and shows their suitability for simulating complex, non-uniform, and dynamical strongly correlated systems.

Findings

Analytic expressions for hopping and interaction parameters derived.

Programmable lattices can emulate Hubbard models with arbitrary basis.

Experimental parameters identified for practical quantum simulation.

Abstract

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 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) 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 correlation 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 arbitrary basis, concluding that programmable optical lattices are suitable for this purpose. We discuss how programmable optical lattices can be used for quantum simulation of dynamical multi-band Hubbard models that represent complicated compounds, impurities, and non-equilibrium physics.