Realizing non-Abelian gauge potentials in optical square lattices: Application to atomic Chern insulators

TL;DR

This paper proposes a method to engineer non-Abelian gauge potentials in optical lattices, enabling simulation of topological insulators like Chern insulators using cold atoms, with potential applications in quantum simulation.

Contribution

It introduces a scheme to realize non-Abelian gauge potentials in square optical lattices, facilitating the simulation of the Haldane model and quantum Hall phases with cold atoms.

Findings

Demonstrated mapping of the Haldane model to matrix hopping operators on a square lattice

Proposed laser-assisted tunneling techniques for implementing non-Abelian gauge fields

Showed potential to realize Chern insulators with cold atom systems

Abstract

We describe a scheme to engineer non-Abelian gauge potentials on a square optical lattice using laser-induced transitions. We emphasize the case of two-electron atoms, where the electronic ground state g is laser coupled to a metastable state e within a state-dependent optical lattice. In this scheme, the alternating pattern of lattice sites hosting g and e states depict a checkerboard structure, allowing for laser-assisted tunneling along both spatial directions. In this configuration, the nuclear spin of the atoms can be viewed as a "flavor" quantum number undergoing non-Abelian tunneling along nearest-neighbor links. We show that this technique can be useful to simulate the equivalent of the Haldane quantum Hall model using cold atoms trapped in square optical lattices, offering an interesting route to realize Chern insulators. The emblematic Haldane model is particularly suited to investigate the physics of topological insulators, but requires, in its original form, complex hopping terms beyond nearest-neighboring sites. In general, this drawback inhibits a direct realization with cold atoms, using standard laser-induced tunneling techniques. We demonstrate that a simple mapping allows to express this model in terms of matrix hopping operators, that are defined on a standard square lattice. This mapping is investigated for two models that lead to anomalous quantum Hall phases. We discuss the practical implementation of such models, exploiting laser-induced tunneling methods applied to the checkerboard optical lattice.