Relativistic quantum effects of Dirac particles simulated by ultracold atoms

Abstract

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.

Dynamics of Weyl quasiparticles in an optical lattice

“…Notably, the 2D atomic Dirac fermions and the related topological phase transition [18][19][20][21][22][23] have been experimentally observed by several groups [24][25][26]. The system can be characterized by the winding number defined by [27] …”

Chiral universality class of normal-superconducting and exciton condensation transitions on surface of topological insulator

“…The Dirac semimetal in optically trapped cold atoms [56] offers a well-controlled system in which this phenomenon occurs both for the repulsive interaction (chiral symmetry breaking) and in particular for the attractive one (superconductivity) because there is no Coulomb repulsion, as the atoms are neutral.…”

“…In addition, a Dirac semimetal was realized in a cold atom system [56] (following the realization in 2D known as synthetic graphene). Interestingly, the sign and strength of the interaction can be controlled.…”

“…Interestingly, the sign and strength of the interaction can be controlled. The Dirac semimetal in optically trapped cold atom systems [56] is well suited to studying this fascinating phenomenon, offering a well-controlled system in which this phenomenon occurs both for repulsive interaction (chiral symmetry breaking) and attractive interaction (superconductivity).…”

Particle-number fractionalization of a one-dimensional atomic Fermi gas with synthetic spin-orbit coupling

“…On the other hand, quantum simulation of the relativistic Dirac Hamiltonian by using ultracold atomic gases has recently attracted great interest [15]. For example, ultracold fermionic atoms trapped in a honeycomb optical lattice (OL) were theoretically proposed to behave as massless and massive Dirac fermions [16] and were confirmed in a * zwang@hku.hk † slzhu@scnu.edu.cn recent experiment [17].…”