An Optical-Lattice-Based Quantum Simulator For Relativistic Field Theories and Topological Insulators

Abstract

We present a proposal for a versatile cold-atom-based quantum simulator of relativistic fermionic theories and topological insulators in arbitrary dimensions. The setup consists of a spin-independent optical lattice that traps a collection of hyperfine states of the same alkaline atom, to which the different degrees of freedom of the field theory to be simulated are then mapped. We show that the combination of bi-chromatic optical lattices with Raman transitions can allow the engineering of a spin-dependent tunneling of the atoms between neighboring lattice sites. These assisted-hopping processes can be employed for the quantum simulation of various interesting models, ranging from non-interacting relativistic fermionic theories to topological insulators. We present a toolbox for the realization of different types of relativistic lattice fermions, which can then be exploited to synthesize the majority of phases in the periodic table of topological insulators.

24 pages, 6 figures

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Cited by in corpus (111)

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• Topological Bands for Ultracold Atoms
• Quantum Algorithms for Quantum Field Theories
• Quantum Simulations of Lattice Gauge Theories using Ultracold Atoms in Optical Lattices
• Ultracold Quantum Gases and Lattice Systems: Quantum Simulation of Lattice Gauge Theories
• Non-Abelian gauge fields and topological insulators in shaken optical lattices
• Quantum simulation of an extra dimension
• Topological quantum matter with cold atoms
• A cold-atom quantum simulator for SU(2) Yang-Mills lattice gauge theory
• Artificial gauge fields in materials and engineered systems
• Quantum simulations of gauge theories with ultracold atoms: local gauge invariance from angular momentum conservation
• Review on novel methods for lattice gauge theories
• Uhlmann Phase as a Topological Measure for One-Dimensional Fermion Systems
• Optical Abelian Lattice Gauge Theories
• Quantum simulation of 2d topological physics using orbital-angular-momentum-carrying photons in a 1d array of cavities
• A Time-Reversal Invariant Topological Phase at the Surface of a 3D Topological Insulator
• Exploring Interacting Topological Insulators with Ultracold Atoms: the Synthetic Creutz-Hubbard Model
• Simulating 2+1d Lattice QED with dynamical matter using ultracold atoms
• Effective theory and emergent $SU(2)$ symmetry in the flat bands of attractive Hubbard models
• Synthesis and Observation of Non-Abelian Gauge Fields in Real Space
• Towards Quantum Simulating QCD
• Extracting the Chern number from the dynamics of a Fermi gas: Implementing a quantum Hall bar for cold atoms
• Tunable topological Weyl semimetal from simple cubic lattices with staggered fluxes
• Quantum simulation of lattice gauge theories using Wilson fermions
• Phase diagram and pair Tomonaga-Luttinger liquid in a Bose-Hubbard model with flat bands
• Fermion-Fermion Scattering in Quantum Field Theory with Superconducting Circuits
• Rydberg-Atom Quantum Simulation and Chern Number Characterization of a Topological Mott Insulator
• Geometry induced pair condensation
• Flat-band many-body localization and ergodicity breaking in the Creutz ladder
• Majorana wavefunction oscillations, fermion parity switches, and disorder in Kitaev chains
• Topological Creutz Ladder in a Resonantly Shaken 1D Optical Lattice
• Topological phases in a two-dimensional lattice: Magnetic field versus spin-orbit coupling
• Order by Disorder in Spin-Orbit Coupled Bose-Einstein Condensates
• Preparation of the SU(3) Lattice Yang-Mills Vacuum with Variational Quantum Methods
• SU(3) Spin-Orbit Coupling in Systems of Ultracold Atoms
• From fractionally charged solitons to Majorana bound states in a one-dimensional interacting model
• Thermal Instability of Protected End States in a 1-D Topological Insulator
• Measuring topology in a laser-coupled honeycomb lattice: From Chern insulators to topological semi-metals
• Topological Bogoliubov excitations in inversion-symmetric systems of interacting bosons
• Coexistence of spin-1/2 and spin-1 Dirac-Weyl fermions in the edge-centered honeycomb lattice
• Quench dynamics and parity blocking in Majorana wires
• Topological Heat Transport and Symmetry-Protected Boson Currents
• Magneto-optics of general pseudospin-s two-dimensional Dirac-Weyl fermions
• Gross-Neveu-Wilson model and correlated symmetry-protected topological phases
• Loop-string-hadron formulation of an SU(3) gauge theory with dynamical quarks
• Double Weyl points and Fermi arcs of topological semimetals in non-Abelian gauge potentials
• Topological phases of quasi-one-dimensional fermionic atoms with a synthetic gauge field
• Analog quantum simulation of generalized Dicke models in trapped ions
• ${\mathbb{Z}}_N$ gauge theories coupled to topological fermions: QED${}_2$ with a quantum-mechanical $\theta$ angle
• 2D spin-orbit coupling for ultracold atoms in optical lattices
• Persistent currents in Dirac fermion rings
• Realizing non-Abelian gauge potentials in optical square lattices: Application to atomic Chern insulators
• Quantum sensors for the generating functional of interacting quantum field theories
• Simulating Effective QED on Quantum Computers
• Simulation of non-Abelian lattice gauge fields with a single component gas
• Topological Quantum Phase Transition in Synthetic Non-Abelian Gauge Potential
• Renormalization group flows for Wilson-Hubbard matter and the topological Hamiltonian
• Lattice-fermionic Casimir effect and topological insulators
• Bright soliton dynamics in Spin Orbit-Rabi coupled Bose-Einstein condensates
• Exploring topological double-Weyl semimetals with cold atoms in optical lattices
• Simulating Dirac fermions with Abelian and non-Abelian gauge fields in optical lattices
• Casimir effect for lattice fermions
• Dynamic Kosterlitz-Thouless transition in 2D Bose mixtures of ultra-cold atoms
• Spiral spin textures of bosonic Mott insulator with SU(3) spin-orbit coupling
• Simulation and measurement of the fractional particle number in one-dimensional optical lattices
• Quantum Simulation of Tunneling in Small Systems
• Topological phase transitions driven by non-Abelian gauge potentials in optical square lattices
• Hidden-symmetry-protected topological phases on a one-dimensional lattice
• Seeing Majorana fermions in time-of-flight images of spinless fermions coupled by s-wave pairing
• Low-energy behaviour of strongly-interacting bosons on a flat-banded lattice above the critical filling factor
• Detection of Chern numbers and entanglement in topological two-species systems through subsystem winding numbers
• Edge mode manipulation through commensurate multifrequency driving
• Topological Wilson-loop area law manifested using a superposition of loops
• Different models of gravitating Dirac fermions in optical lattices
• Tunable Weyl Semi-metal and its Possible Realization in Optical Lattice
• Protecting local and global symmetries in simulating 1+1-D non-abelian gauge theories
• NV-Center Based Digital Quantum Simulation of a Quantum Phase Transition in Topological Insulators
• Dirac fields in curved spacetime as Fermi-Hubbard model with non unitary tunnelings
• Experimental realization of an ideal Floquet disordered system
• Non-equilibrium topological phase transitions in two-dimensional optical lattices
• Semimetal-superfluid quantum phase transitions in 2D and 3D lattices with Dirac points
• Dynamical Detection of Topological Phase Transitions in Short-Lived Atomic Systems
• Simulating Dirac models with ultracold atoms in optical lattices
• Fermion production at the boundary of an expanding universe: a cold-atom gravitational analogue
• Topological chiral currents in the Gross-Neveu model extension
• Fragility of the fractional quantum spin Hall effect in quantum gases
• Kondo effect with Wilson fermions
• Topologically protected mid-gap states induced by impurity in one-dimensional superlattices
• Energy spectra of two interacting fermions with spin-orbit coupling in a harmonic trap
• Flat bands and $Z_2$ topological phases in a non-Abelian kagome lattice
• Optical lattice implementation scheme of a bosonic topological model with fermionic atoms
• Synthetic-gauge-field-induced resonances and Fulde-Ferrell-Larkin-Ovchinnikov states in a one-dimensional optical lattice
• Simulation of two-flavors symmetry-locking phases in ultracold fermionic mixtures
• Tuning the Drude weight of Dirac-Weyl fermions in one-dimensional ring traps
• Quantum walks accompanied by spin flipping in one-dimensional optical lattices
• Valley-dependent gauge fields for ultracold atoms in square optical superlattices
• Time and spatial parity operations with trapped ions
• Efficient algorithm to compute the Berry conductivity
• Topological multiferroic phases in the extended Kane-Mele-Hubbard Model in the Hofstadter regime
• Manipulating matter waves in an optical superlattice
• Phase diagram and non-Abelian symmetry locking for fermionic mixtures with unequal interactions
• Large-$S$ and tensor-network methods for strongly-interacting topological insulators
• Majorana Zero Modes in Fermionic Wires coupled by Aharonov-Bohm Cages
• Cold atoms meet lattice gauge theory
• Effects of the Hubbard interaction on the quantum metric
• Cold atoms in U(3) gauge potentials
• Fast and selective inter-band transfer of ultracold atoms in bichromatic lattices permitting Dirac points
• Quantum phase transitions on the hexagonal lattice
• Superpositions in Atomic Quantum Rings
• High-Precision Phase Control of an Optical Lattice with up to 50 dB Noise Suppression