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.

22 pages, review article in Frontiers of Physics: Proceedings on Quantum Dynamics of Ultracold Atoms

References in corpus (62)

• Electric Field Effect in Atomically Thin Carbon Films
• Non-Abelian Anyons and Topological Quantum Computation
• Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms
• Chiral tunneling and the Klein paradox in graphene
• Quantized Anomalous Hall Effect in Magnetic Topological Insulators
• Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond
• Theory of ultracold Fermi gases
• Direct observation of Anderson localization of matter-waves in a controlled disorder
• An Open-System Quantum Simulator with Trapped Ions
• Quantum Simulation of Antiferromagnetic Spin Chains in an Optical Lattice
• Quantum Anomalous Hall Effect in Hg${}_{1-y}$Mn${}_y$Te Quantum Wells
• Quantum Anomalous Hall Effect in Graphene from Rashba and Exchange Effects
• Spin-Orbit Coupled Spinor Bose-Einstein Condensates
• Flat bands and Wigner crystallization in the honeycomb optical lattice
• A Bose-Einstein Condensate in a Uniform Light-induced Vector Potential
• Non-Abelian gauge potentials for ultra-cold atoms with degenerate dark states
• Multi-Component Quantum Gases in Spin-Dependent Hexagonal Lattices
• Observing Zitterbewegung for photons near the Dirac point of a two-dimensional photonic crystal
• Itinerant Ferromagnetism in a Fermi Gas of Ultracold Atoms
• Dirac Equation and Quantum Relativistic Effects in a Single Trapped Ion
• Simulation and detection of Dirac fermions with cold atoms in an optical lattice
• Spin-orbit coupled Bose-Einstein condensates
• Quantum Computation Using Vortices and Majorana Zero Modes of a $p_x$ + $i{p}_y$ Superfluid of Fermionic Cold Atoms
• Spin Hall effects for cold atoms in a light induced gauge potential
• Zitterbewegung of electronic wave packets in semiconductor nanostructures
• The $p_{x,y}$-orbital counterpart of graphene: cold atoms in the honeycomb optical lattice
• Observing Zitterbewegung in Ultracold Atoms
• Quantum simulation of the Klein paradox with trapped ions
• Non-Abelian optical lattices: Anomalous quantum Hall effect and Dirac Fermions
• Dirac-point engineering and topological phase transitions in honeycomb optical lattices
• Effect of Induced Spin-Orbit Coupling for Atoms via Laser Fields
• Quantum simulation of cosmic inflation in two-component Bose-Einstein condensates
• Orbital analogue of quantum anomalous Hall effect in $p$-band systems
• Wilson Fermions and Axion Electrodynamics in Optical Lattices
• Cold atom simulation of interacting relativistic quantum field theories
• Generalized Rashba spin-orbit coupling for cold atoms
• Realizing and Detecting the Haldane's Quantum Hall effect with Ultracold Atoms
• Probing non-Abelian statistics of Majorana fermions in ultracold atomic superfluid
• Staggered-Vortex Superfluid of Ultracold Bosons in an Optical Lattice
• BCS-BEC crossover on the two-dimensional honeycomb lattice
• Ultracold Fermions in a Graphene-Type Optical Lattice
• Zitterbewegung (trembling motion) of electrons in semiconductors: a Review
• Quasi-relativistic behavior of cold atoms in light fields
• Effective magnetic fields in degenerate atomic gases induced by light beams with orbital angular momenta
• Ultracold atomic gas in non-Abelian "magnetic" fields: the quantum Hall effect supremacy
• Ultracold atomic gases in non-Abelian gauge potentials: The case of constant Wilson loop
• Photon-assisted electron transport in graphene
• Simulating Wess-Zumino Supersymmetry Model in Optical Lattices
• Atomic Zitterbewegung
• Practical scheme for a light-induced gauge field in an atomic Bose gas
• Delocalization of relativistic Dirac particles in disordered one-dimensional systems and its implementation with cold atoms
• Massless Dirac Fermions in a Square Optical Lattice
• Supersymmetry and Goldstino-like Mode in Bose-Fermi Mixtures
• Quantum anomalous Hall states in the $p$-orbital honeycomb optical lattices
• Topology-induced phase transitions in quantum spin Hall lattices
• Confining stationary light: Dirac dynamics and Klein tunneling
• Non-abelian anyons from degenerate Landau levels of ultracold atoms in artificial gauge potentials
• Two-Dimensional Electron Gas with Cold Atoms in Non-Abelian Gauge Potentials
• Quantum walks and quantum simulations with Bloch oscillating spinor atoms
• Ultracold Superstrings in atomic boson-fermion mixtures
• Relativistic linear stability equations for the nonlinear Dirac equation in Bose-Einstein condensates
• Honeycomb optical lattices with harmonic confinement

Cited by in corpus (24)

• Topological insulator and particle pumping in a one-dimensional shaken optical lattice
• Emergent pseudospin-1 Maxwell fermions with a threefold degeneracy in optical lattices
• Hamiltonian design to prepare arbitrary states of four-level systems
• Wannier-Stark states and Bloch oscillations in the honeycomb lattice
• Robust state preparation in quantum simulations of Dirac dynamics
• Dynamical generation of dark solitons in spin-orbit-coupled Bose-Einstein condensates
• Exploring topological double-Weyl semimetals with cold atoms in optical lattices
• Selected topics of quantum computing for nuclear physics
• Simulating bosonic Chern insulators in one-dimensional optical superlattices
• Simulation and measurement of the fractional particle number in one-dimensional optical lattices
• Goos-Hänchen shifts in spin-orbit-coupled cold atoms
• Particle number fractionalization of a one-dimensional atomic Fermi gas with synthetic spin-orbit coupling
• Simulating Dirac models with ultracold atoms in optical lattices
• Interplay of nonreciprocity and nonlinearity on mean-field energy and dynamics of a Bose-Einstein condensate in a double-well potential
• Dimerized Mott insulators in hexagonal optical lattices
• Dirac fermions in a spinning conical Gödel-type spacetime
• Nonlinear Bloch-Zener oscillations for Bose-Einstein condensates in a Lieb optical lattice
• Triplet superconductivity in 3D Dirac semimetal due to exchange interaction
• Cyclotron dynamics of a Bose-Einstein condensate in a quadruple-well potential with synthetic gauge fields
• Simulating the Klein tunneling of pseudospin-one Maxwell particles with trapped ions
• Photonic cellular automaton simulation of relativistic quantum fields: observation of Zitterbewegung
• Chiral universality class of the normal-superconducting and the exciton condensation transition on the surface of topological insulator
• Recent progress on disorder-induced topological phases
• Dirac fermions with electric dipole moment and position-dependent mass in the presence of a magnetic field generated by magnetic monopoles