# Ultracold Fermions in a Graphene-Type Optical Lattice - Quantum Physics

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Abstract: Some important features of the graphene physics can be reproduced by loadingultracold fermionic atoms in a two-dimensional optical lattice with honeycombsymmetry and we address here its experimental feasibility. We analyze in greatdetails the optical lattice generated by the coherent superposition of threecoplanar running laser waves with respective angles $2\pi-3$. The correspondingband structure displays Dirac cones located at the corners of the Brillouinzone and close to half-filling this system is well described by massless Diracfermions. We characterize their properties by accurately deriving thenearest-neighbor hopping parameter $t 0$ as a function of the optical latticeparameters. Our semi-classical instanton method proves in excellent agreementwith an exact numerical diagonalization of the full Hamilton operator in thetight-binding regime. We conclude that the temperature range needed to accessthe Dirac fermions regime is within experimental reach. We also analyzeimperfections in the laser configuration as they lead to optical latticedistortions which affect the Dirac fermions. We show that the Dirac cones dosurvive up to some critical intensity or angle mismatches which are easilycontrolled in actual experiments. In the tight-binding regime, we predict, andnumerically confirm, that these critical mismatches are inversely proportionalto the square-root of the optical potential strength. We also briefly discussthe interesting possibility of fine-tuning the mass of the Dirac fermions bycontrolling the laser phase in an optical lattice generated by the incoherentsuperposition of three coplanar independent standing waves with respectiveangles $2\pi-3$.

Autor: Kean Loon Lee, Benoit Gremaud, Rui Han, Berthold-Georg Englert, Christian Miniatura

Fuente: https://arxiv.org/