Quantum simulation of an extra dimension

Abstract

We present a general strategy to simulate a D+1-dimensional quantum system using a D-dimensional one. We analyze in detail a feasible implementation of our scheme using optical lattice technology. The simplest non-trivial realization of a fourth dimension corresponds to the creation of a bivolume geometry. We also propose single- and many-particle experimental signatures to detect the effects of the extra dimension.

5 pages, 3 figures, revtex style;v2 minor changes, references added

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Cited by in corpus (212)

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• Visualizing edge states with an atomic Bose gas in the quantum Hall regime
• Synthetic gauge fields in synthetic dimensions
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• Photonic topological pumping through the edges of a dynamical four-dimensional quantum Hall system
• Synthetic Dimension in Photonics
• Simulating Lattice Gauge Theories within Quantum Technologies
• Quantum Simulations of Lattice Gauge Theories using Ultracold Atoms in Optical Lattices
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• A single photonic cavity with two independent physical synthetic dimensions
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• Simulating Compact Quantum Electrodynamics with ultracold atoms: Probing confinement and nonperturbative effects
• Four-Dimensional Quantum Hall Effect with Ultracold Atoms
• Artificial gauge fields in materials and engineered systems
• Quantum simulations of gauge theories with ultracold atoms: local gauge invariance from angular momentum conservation
• Optical Abelian Lattice Gauge Theories
• Direct observation of chiral currents and magnetic reflection in atomic flux lattices
• Optomechanical creation of magnetic fields for photons on a lattice
• Circuit Implementation of a Four-Dimensional Topological Insulator
• Experimental band structure spectroscopy along a synthetic dimension
• Atomic Bose-Einstein condensate in a twisted-bilayer optical lattice
• Exploring Interacting Topological Insulators with Ultracold Atoms: the Synthetic Creutz-Hubbard Model
• Higher-order topological insulators in synthetic dimensions
• Topologically Enhanced Harmonic Generation in a Nonlinear Transmission Line Metamaterial
• Synthetic Dimensions for Cold Atoms from Shaking a Harmonic Trap
• Gauge-invariant implementation of the Abelian Higgs model on optical lattices
• Experimental Realization of Weyl Exceptional Rings in a Synthetic Three-Dimensional Non-Hermitian Phononic Crystal
• Realizing Su-Schrieffer-Heeger topological edge states in Rydberg-atom synthetic dimensions
• Giant Atoms in a Synthetic Frequency Dimension
• Production of quantum degenerate strontium gases: Larger, better, faster, colder
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• Topological fractional pumping with alkaline-earth(-like) ultracold atoms
• Ferromagnetic hybrid nodal loop and switchable type-I and type-II Weyl fermions in two-dimension
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• Synthetic dimension band structures on a Si CMOS photonic platform
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• Realization of a cross-linked chiral ladder with neutral fermions in an optical lattice by orbital-momentum coupling
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• Boundary states of 4D topological matter: Emergence and full 3D-imaging of nodal Seifert surfaces
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• Nonlinear states and dynamics in a synthetic frequency dimension
• A comprehensive review on developments of synthetic dimensions
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• Gross-Neveu-Wilson model and correlated symmetry-protected topological phases
• Multi-dimensional band structure spectroscopy in the synthetic frequency dimension
• Artificial non-Abelian lattice gauge fields for photons in the synthetic frequency dimension
• Three-dimensional Chiral Lattice Fermion in Floquet Systems
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• Reservoir spectroscopy of 5s5p ${}^3$P${}_2$ - 5s$n$d ${}^3$D${}_{1,2,3}$ transitions in strontium
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• Spin-orbit-coupled spinor gap solitons in Bose-Einstein condensates
• Dimensional crossovers and Casimir forces for the Bose gas in anisotropic optical lattices
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• Six-dimensional time-space crystalline structures
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• The resonant state at filling factor ν = 1/2 in chiral fermionic ladders
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• Superfluid Vortices in Four Spatial Dimensions
• Topological phase transitions in four dimensions
• Tensor monopoles and negative magnetoresistance effect in optical lattices
• Topological Devil's staircase in atomic two-leg ladders
• Non-Abelian quantum geometric tensor in degenerate topological semimetals
• Quantum magnetism of ultracold atoms with a dynamical pseudospin degree of freedom
• Weyl singularities in polaritonic multi-terminal Josephson junctions
• Synthetic dimensions and topological chiral currents in mesoscopic rings
• Quantum search with interacting Bose-Einstein condensates
• Optical interface states protected by synthetic Weyl points
• Periodic driving induced helical Floquet channels with ultracold atoms in momentum space
• Topological chiral currents in the Gross-Neveu model extension
• Synthetic ${\mathbb{Z}}_2$ gauge theories based on parametric excitations of trapped ions
• Enhanced repulsively bound atom pairs in topological optical lattice ladders
• Inseparable time-crystal geometries on the Möbius strip
• The frequency of the ultranarrow ${}^1{\text{S}}_0-{}^3{\text{P}}_2$ transition in ${}^{87}\text{Sr}$
• Robustness of discrete semifluxons in closed Bose-Hubbard chains
• Exploring helical phases of matter in bosonic ladders
• Simulating artificial one-dimensional physics with ultra-cold fermionic atoms: three exemplary themes
• Synthetic gauge field in two interacting ultracold atomic gases without an optical lattice
• Optical lattice for tripod-like atomic level structure
• Flat-band-induced superconductivity in synthetic bilayer optical lattices
• Simulating quantum transport with ultracold atoms and interaction effects
• Interaction-induced exotic vortex states in an optical lattice clock with spin-orbit coupling
• Local Quantum Thermometry using Unruh-De Witt detectors
• Exact diagonalization of cubic lattice models in commensurate Abelian magnetic fluxes and translational invariant non-Abelian potentials
• Onset of pseudogap and density wave in a system with a closed Fermi surface
• The Coming Decades of Quantum Simulation
• Simulation of two-flavors symmetry-locking phases in ultracold fermionic mixtures
• Four-dimensional Floquet topological insulator with an emergent second Chern number
• Kinetic derivation of generalized phase space Chern-Simons theory
• Spin-tensor Meissner currents of ultracold bosonic gas in an optical lattice
• Meissner effect in Fock space
• Simulating two-dimensional dynamics within a large-size atomic spin
• Synthetic Hall tube of interacting fermions
• Creating high-dimensional topological physics using a single ring resonator
• Topological charge pumping with subwavelength Raman lattices
• Non-Hermitian synthetic lattices with light-matter coupling
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• Synthetic-lattice Bloch wave dynamics in a single-mode microwave resonator
• Few-particle systems: An analysis of some strongly correlated states
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• Geometry-Induced Vacuum Polarization and Mode Shifts in Maxwell-Klein-Gordon Theory
• Encoding a topological gauge theory on a ring-shaped Raman-coupled Bose gas
• Ultracold atomic lattice systems for simulating topological phases: A review
• Synthetic Weyl points in generalized parameter space and their topological properties
• Characterizing the transition from topology to chaos in a kicked quantum system
• Preparing Code States via Seed-Entangler-Enriched Sequential Quantum Circuits: Application to Tetra-Digit Topological Error-Correcting Codes
• Quantum States and Spectra of Small Cylindrical and Toroidal Lattices
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