Different models of gravitating Dirac fermions in optical lattices
arXiv:1612.03076 · doi:10.1140/epjst/e2016-60390-y
Abstract
In this paper I construct the naive lattice Dirac Hamiltonian describing the propagation of fermions in a generic 2D optical metric for different lattice and flux-lattice geometries. First, I apply a top-down constructive approach that we first proposed in [Boada {\it et al.,New J. Phys.} {\bf 13} 035002 (2011)] to the honeycomb and to the brickwall lattices. I carefully discuss how gauge transformations that generalize momentum (and Dirac cone) shifts in the Brillouin zone in the Minkowski homogeneous case can be used in order to change the phases of the hopping. In particular, I show that lattice Dirac Hamiltonian for Rindler spacetime in the honeycomb and brickwall lattices can be realized by considering real and isotropic (but properly position dependent) tunneling terms. For completeness, I also discuss a suitable formulation of Rindler Dirac Hamiltonian in semi-synthetic brickwall and -flux square lattices (where one of the dimension is implemented by using internal spin states of atoms as we originally proposed in [Boada {\it et al.,Phys. Rev. Lett. } {\bf 108} 133001 (2012)] and [Celi {\it et al.,Phys. Rev. Lett. } {\bf 112} 043001 (2012)]).
14 pages, Submitted to EPJ Special Topics for the special issue on "Quantum Gases and Quantum Coherence"; v2: minor changes, figures and references added, similar to the published version, 21 pages, 3 figures
References in corpus (51)
- The electronic properties of graphene
- Chiral tunneling and the Klein paradox in graphene
- Classification of topological insulators and superconductors in three spatial dimensions
- Fiber-optical analogue of the event horizon
- Measurement of stimulated Hawking emission in an analogue system
- Non-standard Hubbard models in optical lattices: a review
- Observation of self-amplifying Hawking radiation in an analog black hole laser
- Hawking radiation from ultrashort laser pulse filaments
- Multi-Component Quantum Gases in Spin-Dependent Hexagonal Lattices
- Dirac Equation and Quantum Relativistic Effects in a Single Trapped Ion
- Atomic Quantum Simulation of U(N) and SU(N) Non-Abelian Lattice Gauge Theories
- Synthetic dimensions and spin-orbit coupling with an optical clock transition
- A cold-atom quantum simulator for SU(2) Yang-Mills lattice gauge theory
- An Aharonov-Bohm interferometer for determining Bloch band topology
- Effects of topological defects and local curvature on the electronic properties of planar graphene
- Zitterbewegung of electronic wave packets in semiconductor nanostructures
- Gibbons-Hawking Effect in the Sonic de Sitter Space-Time of an Expanding Bose-Einstein-Condensed Gas
- Charge inhomogeneities due to smooth ripples in graphene sheets
- An acoustic analog to the dynamical Casimir effect in a Bose-Einstein condensate
- 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
- Atomic quantum simulator for lattice gauge theories and ring exchange models
- Optical Abelian Lattice Gauge Theories
- Wilson Fermions and Axion Electrodynamics in Optical Lattices
- Cold atom simulation of interacting relativistic quantum field theories
- "Cosmological" quasiparticle production in harmonically trapped superfluid gases
- Dirac Equation For Cold Atoms In Artificial Curved Spacetimes
- Tensor Networks for Lattice Gauge Theories with continuous groups
- Zitterbewegung (trembling motion) of electrons in semiconductors: a Review
- Quantum simulation of the Schwinger model: A study of feasibility
- Quasi-relativistic behavior of cold atoms in light fields
- Entanglement renormalization and gauge symmetry
- Lattice Gauge Tensor Networks
- Klein tunneling and Dirac potentials in trapped ions
- Detection of acceleration radiation in a Bose-Einstein condensate
- Analogue of cosmological particle creation in an ion trap
- Weyl-Gauge Symmetry of Graphene
- Semi-synthetic zigzag optical lattice for ultracold bosons
- Observer dependence for the phonon content of the sound field living on the effective curved space-time background of a Bose-Einstein condensate
- Atomic Zitterbewegung
- Quantum simulation of non-trivial topology
- Quantum signature of analog Hawking radiation in momentum space
- Synthetic Dimensions with Magnetic Fields and Local Interactions in Photonic Lattices
- Confining stationary light: Dirac dynamics and Klein tunneling
- Projected Entangled Pair States with non-Abelian gauge symmetries: an SU(2) study
- Chains with loops - synthetic magnetic fluxes and topological order in one-dimensional spin systems
- Double transfer through Dirac points in a tunable honeycomb optical lattice
- Devil's staircases in synthetic dimensions and gauge fields
- Synthetic-gauge-field-induced resonances and Fulde-Ferrell-Larkin-Ovchinnikov states in a one-dimensional optical lattice
Cited by in corpus (9)
- Unruh effect for interacting particles with ultracold atoms
- Probing non-Hermitian phase transitions in curved space via quench dynamics
- Measuring Chern numbers in Hofstadter strips
- Horizon physics of quasi-one-dimensional tilted Weyl cones on a lattice
- Fermion production at the boundary of an expanding universe: a cold-atom gravitational analogue
- Anisotropic optics and gravitational lensing of tilted Weyl fermions
- Dirac equation on a square waveguide lattice with site-dependent coupling strengths and the gravitational Aharonov-Bohm effect
- Nonlinear entanglement growth in inhomogeneous spacetimes
- Quantum dynamics in 1D lattice models with synthetic horizons