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Ultracold fermions in a graphene-type optical lattice

Kean Loon Lee (李健伦), Benoît Grémaud, Rui Han (韩睿), Berthold-Georg Englert, and Christian Miniatura
Phys. Rev. A 80, 043411 – Published 19 October 2009
Physics logo See Synopsis: An ultracold graphene analog

Abstract

Some important features of the graphene physics can be reproduced by loading ultracold fermionic atoms in a two-dimensional optical lattice with honeycomb symmetry and we address here its experimental feasibility. We analyze in great detail the optical lattice generated by the coherent superposition of three coplanar running laser waves with respective angles 2π/3. The corresponding band structure displays Dirac cones located at the corners of the Brillouin zone and close to half-filling this system is well described by massless Dirac fermions. We characterize their properties by accurately deriving the nearest-neighbor hopping parameter t0 as a function of the optical lattice parameters. Our semiclassical instanton method proves in excellent agreement with an exact numerical diagonalization of the full Hamilton operator in the tight-binding regime. We conclude that the temperature range needed to access the Dirac fermions regime is within experimental reach. We also analyze imperfections in the laser configuration as they lead to optical lattice distortions which affect the Dirac fermions. We show that the Dirac cones do survive up to some critical intensity or angle mismatches which are easily controlled in actual experiments. In the tight-binding regime, we predict, and numerically confirm, that these critical mismatches are inversely proportional to the square root of the optical potential strength. We also briefly discuss the interesting possibility of fine tuning the mass of the Dirac fermions by controlling the laser phase in an optical lattice generated by the incoherent superposition of three coplanar independent standing waves with respective angles 2π/3.

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  • Received 23 June 2009

DOI:https://doi.org/10.1103/PhysRevA.80.043411

©2009 American Physical Society

Synopsis

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An ultracold graphene analog

Published 26 October 2009

The properties of graphene might be studied from another angle by putting ultracold atoms into a hexagonal optical lattice.

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Authors & Affiliations

Kean Loon Lee (李健伦)1,2,3,*, Benoît Grémaud2,1,4, Rui Han (韩睿)1, Berthold-Georg Englert1,4, and Christian Miniatura5,1,4

  • 1Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543, Singapore
  • 2Laboratoire Kastler-Brossel, UPMC-Paris 6, ENS, CNRS; 4 Place Jussieu, F–75005 Paris, France
  • 3NUS Graduate School for Integrative Sciences and Engineering, National University of Singapore, Singapore 117597, Singapore
  • 4Department of Physics, National University of Singapore, 2 Science Drive 3, Singapore 117542, Singapore
  • 5Institut Non Linéaire de Nice, UMR 6618, UNS, CNRS; 1361 route des Lucioles, 06560 Valbonne, France

  • *leekeanl@sps.nus.edu.sg

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Issue

Vol. 80, Iss. 4 — October 2009

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