Simulating Dirac fermions with Abelian and non-Abelian gauge fields in optical lattices

TL;DR

This paper proposes a simplified optical lattice setup to simulate 2+1 dimensional Dirac fermions with gauge fields, enabling experimental exploration of relativistic quantum phenomena using laser-modulated honeycomb lattices.

Contribution

It introduces a method to realize the full Dirac Hamiltonian with external potentials in optical lattices through laser intensity modulations, avoiding complex additional fields.

Findings

All external potentials can be generated from existing lattice couplings.

The setup requires only spatial laser intensity modulations.

Several experiments are proposed to observe Dirac fermion properties.

Abstract

In this work we present an optical lattice setup to realize a full Dirac Hamiltonian in 2+1 dimensions. We show how all possible external potentials coupled to the Dirac field can arise from perturbations of the existing couplings of the honeycomb lattice model, without the need of additional laser fields. This greatly simplifies the proposed implementations, requiring only spatial modulations of the intensity of the laser beams. We finally suggest several experiments to observe the properties of the Dirac field in the setup.