Relativistic quantum mechanics with trapped ions

Abstract

We consider the quantum simulation of relativistic quantum mechanics, as described by the Dirac equation and classical potentials, in trapped-ion systems. We concentrate on three problems of growing complexity. First, we study the bidimensional relativistic scattering of single Dirac particles by a linear potential. Furthermore, we explore the case of a Dirac particle in a magnetic field and its topological properties. Finally, we analyze the problem of two Dirac particles that are coupled by a controllable and confining potential. The latter interaction may be useful to study important phenomena as the confinement and asymptotic freedom of quarks.

17 pages, 4 figures

References in corpus (25)

• Chiral tunneling and the Klein paradox in graphene
• Cold Quark Matter
• Dirac Equation and Quantum Relativistic Effects in a Single Trapped Ion
• Zitterbewegung of electronic wave packets in semiconductor nanostructures
• Exact Mapping of the 2+1 Dirac Oscillator onto the Jaynes-Cummings Model: Ion-Trap Experimental Proposal
• Observing Zitterbewegung in Ultracold Atoms
• Quantum simulation of the Klein paradox with trapped ions
• Unified description of the Zitterbewegung for spintronic, graphene and superconducting systems
• Non-Abelian optical lattices: Anomalous quantum Hall effect and Dirac Fermions
• Wilson Fermions and Axion Electrodynamics in Optical Lattices
• Cold atom simulation of interacting relativistic quantum field theories
• Dirac Equation For Cold Atoms In Artificial Curved Spacetimes
• Zitterbewegung (trembling motion) of electrons in semiconductors: a Review
• Klein tunneling and Dirac potentials in trapped ions
• Analogue of cosmological particle creation in an ion trap
• Atomic Zitterbewegung
• Delocalization of relativistic Dirac particles in disordered one-dimensional systems and its implementation with cold atoms
• Confining stationary light: Dirac dynamics and Klein tunneling
• On the effective Dirac dynamics of ultracold atoms in bichromatic optical lattices
• Zitterbewegung of relativistic electrons in a magnetic field and its simulation by trapped ions
• Photon wave function and zitterbewegung
• Zitterbewegung of optical pulses in nonlinear frequency conversion
• Parity-relevant Zitterbewegung and quantum simulation by a single trapped ion
• Classical zitterbewegung in reduced plasma dynamics
• Zitterbewegung-like effect near the Dirac point in metamaterials and photonic crystals

Cited by in corpus (51)

• Quantum information processing with superconducting circuits: a review
• Quantum Simulation of the Ultrastrong Coupling Dynamics in Circuit QED
• Quantum Simulation of Interacting Fermion Lattice Models in Trapped Ions
• Quantum Simulation of Quantum Field Theories in Trapped Ions
• Digital Quantum Simulation of the Holstein Model in Trapped Ions
• A dispersion and norm preserving finite difference scheme with transparent boundary conditions for the Dirac equation in (1+1)D
• Quantum Simulation of the Majorana Equation and Unphysical Operations
• Quantum Simulations of Relativistic Quantum Physics in Circuit QED
• Analog quantum simulation of generalized Dicke models in trapped ions
• Tachyon physics with trapped ions
• Staggered grid leap-frog scheme for the (2+1)D Dirac equation
• Statistical proerties of the two-dimensional Feshbach-illars oscillator (FVO) in the rotating cosmic string
• Relativistic Killingbeck Energy States Under an External Magnetic Fields
• The noncommutative quantum Hall effect with anomalous magnetic moment in three different relativistic scenarios
• Localization behavior of Dirac particles in disordered graphene superlattices
• Lattice-layer entanglement in Bernal-stacked bilayer graphene
• Chiral oscillations in the non-relativistic regime
• Quantum Simulation of Noncausal Kinematic Transformations
• Quantum transitions and quantum entanglement from Dirac-like dynamics simulated by trapped ions
• Two-mode generalization of the Jaynes-Cummings and Anti-Jaynes-Cummings models
• $SU(2)\otimes SU(2)$ bi-spinor structure entanglement induced by a step potential barrier scattering in two-dimensions
• Simulating Dirac models with ultracold atoms in optical lattices
• A generalized Jaynes-Cummings model: The relativistic parametric amplifier and a single trapped ion
• Relativistic and nonrelativistic Landau levels for the noncommutative quantum Hall effect with anomalous magnetic moment in a conical Gödel-type spacetime
• Entanglement Measures in Ion-Trap Quantum Simulators without Full Tomography
• Graphene lattice-layer entanglement under non-Markovian phase noise
• Photonic realization of the deformed Dirac equation via the segmented graphene nanoribbons under inhomogeneous strain
• Langmuir waves dispersion in semi-relativistic spinless quantum plasmas
• Topological Qubits with Majorana Fermions in Trapped Ions
• Matrix diagonalization and exact solution of the k-photon Jaynes-Cummings model
• Encoding relativistic potential dynamics into free evolution
• Massless Dirac Fermions in Electromagnetic Field
• Quantum Simulation of the Two-Dimensional Weyl Equation in a Magnetic Field
• The nonrelativistic limit of the Majorana equation and its simulation in trapped ions
• Algebraic approach to the Tavis-Cummings model with three modes of oscillation
• Schrödinger cat and Werner state disentanglement simulated by trapped ion systems
• Time and spatial parity operations with trapped ions
• Phase-space elementary information content of confined Dirac spinors
• Switchable Particle Statistics with an Embedding Quantum Simulator
• Toward simulating quantum field theories with controlled phonon-ion dynamics: A hybrid analog-digital approach
• Algebraic approach and Berry phase of a Hamiltonian with a general $SU(1,1)$ symmetry
• $Sp(4,R)$ algebraic approach of the most general Hamiltonian of a two-level system in two-dimensional geometry
• Simulating the Klein tunneling of pseudospin-one Maxwell particles with trapped ions
• Engineering an Effective Three-spin Hamiltonian in Trapped-ion Systems for Applications in Quantum Simulation
• Berry phase of the Tavis-Cummings model with three modes of oscillation
• Dirac bi-spinor entanglement under local noise and its simulation by Jaynes-Cummings interactions
• Topological Phase Transitions in Superfluids Near Black Hole Horizons
• Non-locality of energy separating transformations for Dirac electrons in a magnetic field
• Analysis of Spin-1/2 Particle Scattering in a Spinning Cosmic String Spacetime with Torsion, Curvature, and a Coulomb Potential
• Bipartite entanglement of localized separated systems
• Realizing topological relativistic dynamics with slow light polaritons at room temperature