Quantum simulation is a powerful tool to study a variety of problems in physics, ranging from high-energy physics to condensed-matter physics. In this article, we review the recent theoretical and experimental progress in quantum simulation of Dirac equation with tunable parameters by using ultracold neutral atoms trapped in optical lattices or subject to light-induced synthetic gauge fields. The effective theories for the quasiparticles become relativistic under certain conditions in these systems, making them ideal platforms for studying the exotic relativistic effects. We focus on the realization of one, two, and three dimensional Dirac equations as well as the detection of some relativistic effects, including particularly the well-known Zitterbewegung effect and Klein tunneling. The realization of quantum anomalous Hall effects is also briefly discussed.Quantum simulation is a powerful tool to study a variety of problems in physics, ranging from high-energy physics to condensed-matter physics. In this article, we review the recent theoretical and experimental progress in quantum simulation of Dirac equation with tunable parameters by using ultracold neutral atoms trapped in optical lattices or subject to light-induced synthetic gauge fields. The effective theories for the quasiparticles become relativistic under certain conditions in these systems, making them ideal platforms for studying the exotic relativistic effects. We focus on the realization of one, two, and three dimensional Dirac equations as well as the detection of some relativistic effects, including particularly the well-known Zitterbewegung effect and Klein tunneling. The realization of quantum anomalous Hall effects is also briefly discussed.

arXiv:1203.5949Frontiers of PhysicsDec 12, 201169 citations

Quantum simulation with ultracold atoms

Laurent Sanchez-Palencia

Aug 1, 20200 citations

Quantum walks and quantum simulations with Bloch-oscillating spinor atoms

Dirk Witthaut

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 $1+1$ dimensions. Thus it becomes possible to simulate relativistic effects such as Zitterbewegung and Klein tunneling.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 $1+1$ dimensions. Thus it becomes possible to simulate relativistic effects such as Zitterbewegung and Klein tunneling.

arXiv:1010.2514Physical Review ASep 8, 201037 citations

Quantum Mechanics of Dirac Particles

World Scientific lecture notes in physicsSep 1, 20200 citations

Direct observation of zitterbewegung in a Bose–Einstein condensate

L J LeBlanc, M C Beeler, K Jiménez-García +4 more

Zitterbewegung, a force-free trembling motion first predicted for relativistic fermions like electrons, was an unexpected consequence of the Dirac equation's unification of quantum mechanics and special relativity. Though the oscillatory motion's large frequency and small amplitude have precluded its measurement with electrons, zitterbewegung is observable via quantum simulation. We engineered an environment for 87 Rb Bose–Einstein condensates where the constituent atoms behaved like relativistic particles subject to the one-dimensional Dirac equation. With direct imaging, we observed the sub-micrometre trembling motion of these clouds, demonstrating the utility of neutral ultracold quantum gases for simulating Dirac particles.Zitterbewegung, a force-free trembling motion first predicted for relativistic fermions like electrons, was an unexpected consequence of the Dirac equation's unification of quantum mechanics and special relativity. Though the oscillatory motion's large frequency and small amplitude have precluded its measurement with electrons, zitterbewegung is observable via quantum simulation. We engineered an environment for 87 Rb Bose–Einstein condensates where the constituent atoms behaved like relativistic particles subject to the one-dimensional Dirac equation. With direct imaging, we observed the sub-micrometre trembling motion of these clouds, demonstrating the utility of neutral ultracold quantum gases for simulating Dirac particles.

arXiv:1303.0914New Journal of PhysicsJul 3, 2013186 citations

1+1

dimensions. Thus it becomes possible to simulate relativistic effects such as Zitterbewegung and Klein tunneling.