Quantum simulation of a 2D quasicrystal with cold atoms

Abstract

We describe a way to obtain a two-dimensional quasiperiodic tiling with eight-fold symmetry using cold atoms. A series of such optical tilings, related by scale transformations, is obtained for a series of specific values of the chemical potential of the atoms. A theoretical model for the optical system is described and compared with that of the well-known cut-and-project method for the Ammann-Beenker tiling. This type of cold atom structure should allow the simulation of several important lattice models for interacting quantum particles and spins in quasicrystals.

arXiv commentReview article, 12 pages, 14 figures

References in corpus (8)

• Many-Body Physics with Ultracold Gases
• Cold bosonic atoms in optical lattices
• Non-standard Hubbard models in optical lattices: a review
• Quantum critical state in a magnetic quasicrystal
• Quantum Antiferromagnetism in Quasicrystals
• Non-Fermi-Liquid Behavior in Metallic Quasicrystals with Local Magnetic Moments
• Magnetic states induced by electron-electron interactions in a plane quasiperiodic tiling
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Cited by in corpus (14)

• Critical Behavior and Fractality in Shallow One-Dimensional Quasiperiodic Potentials
• Strongly-Interacting Bosons in a Two-Dimensional Quasicrystal Lattice
• Observation of localization of light in photonic quasicrystals of diverse symmetries
• Hubbard Models for Quasicrystalline Potentials
• Thermodynamic Phase Diagram of Two-Dimensional Bosons in a Quasicrystal Potential
• Electronic instabilities in Penrose quasi-crystals: competition, coexistence and collaboration of order
• Two-dimensional optical quasicrystal potentials for ultracold atom experiments
• Properties of the Ammann-Beenker tiling and its square approximants
• Amorphous quantum magnets in a two-dimensional Rydberg atom array
• Revival and Expansion of the Theory of Coherent Lattices
• Stability of quasicrystalline ultracold fermions to dipolar interactions
• Strong Boundary and Trap Potential Effects on Emergent Physics in Ultra-Cold Fermionic Gases
• Emergent aperiodicity in Bose-Bose mixtures induced by spin-dependent periodic potentials
• On the origin of energy gaps in quasicrystalline potentials