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arXiv:cond-mat/0703454 · Physical Review Letters

Simulation and Detection of Dirac Fermions with Cold Atoms in an Optical Lattice

Shi-Liang Zhu, Baigeng Wang, L.-M. Duan

Published Jun 25, 2007• 306 citations
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Abstract

We propose an experimental scheme to simulate and observe relativistic Dirac fermions with cold atoms in a hexagonal optical lattice. By controlling the lattice anisotropy, one can realize both massive and massless Dirac fermions and observe the phase transition between them. Through explicit calculations, we show that both the Bragg spectroscopy and the atomic density profile in a trap can be used to demonstrate the Dirac fermions and the associated phase transition.

DOI
10.1103/physrevlett.98.260402

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We propose an experimental scheme to simulate and observe relativistic Dirac fermions with cold atoms in a hexagonal optical lattice. By controlling the lattice anisotropy, one can realize both massive and massless Dirac fermions and observe the phase transition between them. Through explicit calculations, we show that both the Bragg spectroscopy and the atomic density profile in a trap can be used to demonstrate the Dirac fermions and the associated phase transition.
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We propose the experimental realization of (3+1) relativistic Dirac fermions using ultracold atoms in a rotating optical lattice or, alternatively, in a synthetic magnetic field. This approach has the advantage to give mass to the Dirac fermions by coupling the ultracold atoms to a Bragg pulse. A dimensional crossover from (3+1) to (2+1) Dirac fermions can be obtained by varying the anisotropy of the lattice. We also discuss under which conditions the interatomic potentials give rise to relativistically invariant interactions among the Dirac fermions.
We propose an experimental setup for the observation of quasirelativistic massless fermions. It is based on a T3{\mathcal{T}}_{3}T3​ optical lattice, realized by three pairs of counterpropagating lasers, filled with fermionic cold atoms. We show that in the long wavelength approximation the T3{\mathcal{T}}_{3}T3​ Hamiltonian generalizes the Dirac-Weyl Hamiltonian for the honeycomb lattice, however, with a larger value of the pseudospin S=1S=1S=1. In addition to the Dirac cones, the spectrum includes a dispersionless branch of localized states producing a finite jump in the atomic density. Furthermore, implications for the Landau levels are discussed.
Dirac points lie at the heart of many fascinating phenomena in condensed matter physics, from massless electrons in graphene to the emergence of conducting edge states in topological insulators. At a Dirac point, two energy bands intersect linearly and the particles behave as relativistic Dirac fermions. In solids, the rigid structure of the material sets the mass and velocity of the particles, as well as their interactions. A different, highly flexible approach is to create model systems using fermionic atoms trapped in an optical lattice, a method which so far has only been applied to explore simple lattice structures. In my talk I will report on the creation of Dirac points with adjustable properties in a tunable honeycomb optical lattice [1]. Using momentum-resolved interband transitions, we observe a minimum band gap inside the Brillouin zone at the position of the Dirac points. We exploit the unique tunability of our lattice potential to adjust the effective mass of the Dirac fermions by breaking the inversion symmetry of the lattice. Moreover, changing the lattice anisotropy allows us to move the position of the Dirac points inside the Brillouin zone. When increasing the anisotropy beyond a critical limit, the two Dirac points merge and annihilate each other. We map out this topological transition in lattice parameter space and find excellent agreement with ab initio calculations. Our results not only pave the way to model materials where the topology of the band structure plays a crucial role, but also provide the possibility to explore many-body phases resulting from the interplay of complex lattice geometries with interactions.
We propose a feasible experimental scheme to realize a three-dimensional chiral topological insulator with cold fermionic atoms in an optical lattice, which is characterized by an integer topological invariant distinct from the conventional Z(2) topological insulators and has a remarkable macroscopic zero-energy flat band. To probe its property, we show that its characteristic surface states--the Dirac cones--can be probed through time-of-flight imaging or Bragg spectroscopy and the flat band can be detected via measurement of the atomic density profile in a weak global trap. The realization of this novel topological phase with a flat band in an optical lattice will provide a unique experimental platform to study the interplay between interaction and topology and open new avenues for application of topological states.
We present a scheme to realize three-dimensional Dirac-like fermions with an edge-centered cubic optical lattice. We propose a method to construct the optical edge-centered cubic crystals and then determine the parameters required for the description of the systems with a tight-binding model. Interestingly, we show that the low-energy quasiparticles are three-dimensional massive or massless Dirac-like fermions determined by the parameters of the system. In addition, two three-dimensional degenerate flat bands lie between the upper and the lower branches of the Dirac dispersion. Furthermore, we demonstrate that the Dirac dispersion relation and the flat bands can be verified by the density profile measurement.