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.

arXiv comment22 pages, review article in Frontiers of Physics: Proceedings on Quantum Dynamics of Ultracold Atoms

References in corpus (118)

• Electric Field Effect in Atomically Thin Carbon Films
• Two-Dimensional Gas of Massless Dirac Fermions in Graphene
• Topological Insulators
• Experimental Observation of Quantum Hall Effect and Berry's Phase in Graphene
• Non-Abelian Anyons and Topological Quantum Computation
• Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms
• Theory of Bose-Einstein condensation in trapped gases
• 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
• A spin-orbit coupled Bose-Einstein condensate
• Theory of ultracold Fermi gases
• Anderson localization of a non-interacting Bose-Einstein condensate
• Observation of resonance condensation of fermionic atom pairs
• Non-Abelian statistics and topological quantum information processing in 1D wire networks
• Direct observation of Anderson localization of matter-waves in a controlled disorder
• Formation of a Matter-Wave Bright Soliton
• Synthetic magnetic fields for ultracold neutral atoms
• Controlling Spin Exchange Interactions of Ultracold Atoms in Optical Lattices
• An Open-System Quantum Simulator with Trapped Ions
• Transition from a strongly interacting 1D superfluid to a Mott insulator
• Seeing the magnetic monopole through the mirror of topological surface states
• Quantum Simulation of Antiferromagnetic Spin Chains in an Optical Lattice
• Fermionic Superfluidity with Imbalanced Spin Populations and the Quantum Phase Transition to the Normal State
• Creation of effective magnetic fields in optical lattices: The Hofstadter butterfly for cold neutral atoms
• Bragg spectroscopy of a Bose-Einstein condensate
• Majorana Fermions in Equilibrium and Driven Cold Atom Quantum Wires
• Quantum Anomalous Hall Effect in Hg${}_{1-y}$Mn${}_y$Te Quantum Wells
• Quantum simulation of the Dirac equation
• Quantum Anomalous Hall Effect in Graphene from Rashba and Exchange Effects
• Sonic analog of gravitational black holes in Bose-Einstein condensates
• Spin-Orbit Coupled Spinor Bose-Einstein Condensates
• Rapidly Rotating Atomic Gases
• Zitterbewegung, chirality, and minimal conductivity in graphene
• 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
• Fractional quantum Hall states of atoms in optical Lattices
• Cold atoms in non-Abelian gauge potentials: From the Hofstadter "moth" to lattice gauge theory
• The Mott insulator transition in two dimensions
• Disordered quantum gases under control
• 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
• Gauge fields for ultracold atoms in optical superlattices
• Spin-orbit coupled Bose-Einstein condensates
• A synthetic electric force acting on neutral atoms
• Delocalization of a disordered bosonic system by repulsive interactions
• Quantum Computation Using Vortices and Majorana Zero Modes of a $p_x$ + $i{p}_y$ Superfluid of Fermionic Cold Atoms
• Quantized Anomalous Hall Effect in Two-Dimensional Ferromagnets - Quantum Hall Effect from Metal -
• Spin Hall effects for cold atoms in a light induced gauge potential
• Zitterbewegung of electronic wave packets in semiconductor nanostructures
• Massless Dirac-Weyl Fermions in a T_3 Optical Lattice
• The $p_{x,y}$-orbital counterpart of graphene: cold atoms in the honeycomb optical lattice
• Raman processes and effective gauge potentials
• 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
• Slow light in degenerate Fermi gases
• 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
• Flat bands, Dirac cones and atom dynamics in an optical lattice
• Prefect Klein tunneling in anisotropic graphene-like photonic lattices
• Light induced effective magnetic fields for ultra-cold atoms in planar geometries
• 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
• Fractional Quantum Hall States in Ultracold Rapidly Rotating Dipolar Fermi Gases
• Zitterbewegung (trembling motion) of electrons in semiconductors: a Review
• Dirac-Weyl fermions with arbitrary spin in two-dimensional optical superlattices
• Quantum Anomalous Hall Effect with Cold Atoms Trapped in a Square Lattice
• The Nonlinear Dirac Equation in Bose-Einstein Condensates: Foundation and Symmetries
• Quasi-relativistic behavior of cold atoms in light fields
• Chiral confinement in quasirelativistic Bose-Einstein condensates
• 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
• Topological phase transitions in the non-Abelian honeycomb lattice
• Practical scheme for a light-induced gauge field in an atomic Bose gas
• Atomic Zitterbewegung
• Massless Dirac Fermions in a Square Optical Lattice
• Delocalization of relativistic Dirac particles in disordered one-dimensional systems and its implementation with cold atoms
• Supercriticality and Transmission Resonances in the Dirac equation
• Artificial Staggered Magnetic Field for Ultracold Atoms in Optical Lattices
• 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
• Spin-orbit coupled Bose-Einstein condensate in a tilted optical lattice
• 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
• Bose-Einstein Condensate in a Honeycomb Optical Lattice: Fingerprint of Superfluidity at the Dirac Point
• On the effective Dirac dynamics of ultracold atoms in bichromatic optical lattices
• Birefringent break up of Dirac fermions in a square optical lattice
• (3+1) Massive Dirac Fermions with Ultracold Atoms in Optical Lattices
• Quenching through Dirac and semi-Dirac points in optical Lattices: Kibble-Zurek scaling for anisotropic Quantum-Critical systems
• Quantum walks and quantum simulations with Bloch oscillating spinor atoms
• Quantized Anomalous Hall Insulator in a Nanopatterned Two-Dimensional Electron Gas
• Ultracold Superstrings in atomic boson-fermion mixtures
• Relativistic linear stability equations for the nonlinear Dirac equation in Bose-Einstein condensates
• Driven Dirac-like Equation via Mirror Oscillation: Controlled Cold-Atom Zitterbewegung
• Strongly Interacting Two-Dimensional Dirac Fermions
• Simulating high-temperature superconductivity model Hamiltonians with atoms in optical lattices
• Topological quantum phase transitions of attractive spinless fermions in a honeycomb lattice
• Filled Landau levels in neutral quantum gases
• Honeycomb optical lattices with harmonic confinement
• Quantum Hall Effect in Thin Films of Three-Dimensional Topological Insulators

Cited by in corpus (39)

• Light-induced gauge fields for ultracold atoms
• Topological quantum matter with cold atoms
• Scalar, spinor, and photon fields under relativistic cavity motion
• Topological insulator and particle pumping in a one-dimensional shaken optical lattice
• Josephson dynamics of a spin-orbit coupled Bose-Einstein condensate in a double well potential
• Emergent pseudospin-1 Maxwell fermions with a threefold degeneracy in optical lattices
• Simulating and exploring Weyl semimetal physics with cold atoms in a two-dimensional optical lattice
• Hamiltonian design to prepare arbitrary states of four-level systems
• Wannier-Stark states and Bloch oscillations in the honeycomb lattice
• Quantum phases in tunable state-dependent hexagonal optical lattices
• Robust state preparation in quantum simulations of Dirac dynamics
• Floquet engineering and simulating exceptional rings with a quantum spin system
• Zitterbewegung effect in spin-orbit coupled spin-1 ultracold atoms
• Dynamics of Weyl quasiparticles emerged in an optical lattice
• 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
• Generalized Hofstadter model on a cubic optical lattice: From nodal bands to the three-dimensional quantum Hall effect
• Beyond the constant-mass Dirac physics: Solitons, charge fractionization, and the emergence of topological insulators in graphene rings
• Particle number fractionalization of a one-dimensional atomic Fermi gas with synthetic spin-orbit coupling
• Goos-Hänchen shifts in spin-orbit-coupled cold atoms
• 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
• Langmuir waves dispersion in semi-relativistic spinless quantum plasmas
• Dimerized Mott insulators in hexagonal optical lattices
• Dirac fermions in a spinning conical Gödel-type spacetime
• Fractional quantization of charge and spin in topological quantum pumps
• Cyclotron dynamics of a Bose-Einstein condensate in a quadruple-well potential with synthetic gauge fields
• Nonlinear Bloch-Zener oscillations for Bose-Einstein condensates in a Lieb optical lattice
• Valley-dependent gauge fields for ultracold atoms in square optical superlattices
• Triplet superconductivity in 3D Dirac semimetal due to exchange interaction
• Simulating the Klein tunneling of pseudospin-one Maxwell particles with trapped ions
• Chiral universality class of the normal-superconducting and the exciton condensation transition on the surface of topological insulator
• Photonic cellular automaton simulation of relativistic quantum fields: observation of Zitterbewegung
• Simulation of the many-body dynamical quantum Hall effect in an optical lattice
• 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