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arXiv:1710.04416 · Physical Review A

Simulating Dirac models with ultracold atoms in optical lattices

Jean Claude Garreau, Véronique Zehnlé

Published Oct 27, 2017• 12 citations
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Abstract

We present a general model allowing quantum simulation of one-dimensional Dirac models with two- and four-component spinors using ultracold atoms in driven one-dimensional tilted optical latices. The resulting Dirac physics is illustrated by one of its well-known manifestations, zitterbewegung. This general model can be extended and applied with great flexibility to more complex situations.

DOI
10.1103/physreva.96.043627

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We present a general model allowing quantum simulation of one-dimensional Dirac models with two- and four-component spinors using ultracold atoms in driven one-dimensional tilted optical latices. The resulting Dirac physics is illustrated by one of its well-known manifestations, zitterbewegung. This general model can be extended and applied with great flexibility to more complex situations.
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We propose a scheme for the realization of a quantum walker and a quantum simulator for the Dirac equation with ultracold spinor atoms in driven optical lattices. A precise control of the dynamics of the atomic matter wave can be realized using time-dependent external forces. If the force depends on the spin state of the atoms, the dynamics will entangle the inner and outer degrees of freedom, which offers unique opportunities for quantum information and quantum simulation. Here we introduce a method to realize a quantum walker based on the state-dependent transport of spinor atoms and a coherent driving of the internal state. In the limit of weak driving the dynamics are equivalent to that of a Dirac particle in 1+11+11+1 dimensions. Thus it becomes possible to simulate relativistic effects such as Zitterbewegung and Klein tunneling.
The Dirac fermion is an important fundamental particle appearing in high-energy physics and topological insulator physics. In particular, a Dirac fermion in a one-dimensional lattice system exhibits the essential properties of topological physics. However, the system has not been quantum simulated in experiments yet. Herein, we propose a one-dimensional generalized lattice Wilson-Dirac fermion model and study its topological phase structure. We show the experimental setups of an atomic quantum simulator for the model, in which two parallel optical lattices with the same tilt for trapping cold fermion atoms and a laser-assisted hopping scheme are used. Interestingly, we find that the model exhibits nontrivial topological phases characterized by gapless edge modes and a finite winding number in the broad regime of the parameter space. Some of the phase diagrams closely resemble those of the Haldane model. We also discuss topological charge pumping and a lattice Gross-Neveu model in the system of generalized Wilson-Dirac fermions.
We propose a scheme for the quantum simulation of quantum link models in two-dimensional lattices. Our approach considers spinor dipolar gases on a suitably shaped lattice, where the dynamics of particles in the different hyperfine levels of the gas takes place in one-dimensional chains coupled by the dipolar interactions. We show that at least four levels are needed. The present scheme does not require any particular fine-tuning of the parameters. We perform the derivation of the parameters of the quantum link models by means of two different approaches, a nonperturbative one tied to angular-momentum conservation, and a perturbative one. A comparison with other schemes for (2+1)(2+1)(2+1)-dimensional quantum link models present in the literature is discussed. Finally, the extension to three-dimensional lattices is presented, and its subtleties are pointed out.