Four-dimensional photonic lattices and discrete tesseract solitons

Abstract

We theoretically study discrete photonic lattices in more than three dimensions and point out that such systems can exist in continuous three-dimensional (3D) space. We study discrete diffraction in the linear regime, and predict the existence of four-dimensional (4D) tesseract solitons in nonlinear 4D periodic photonic lattices. Finally, we propose a design towards a potential realization of such periodic 4D lattices in experiments.

Submitted to PRL on 14 May 2012

References in corpus (1)

• Quantum simulation of an extra dimension

Cited by in corpus (40)

• Topological Photonics
• Topological Photonics
• Photonic topological pumping through the edges of a dynamical four-dimensional quantum Hall system
• Topological quantum matter in synthetic dimensions
• Photonic Topological Insulator in Synthetic Dimensions
• Synthetic dimensions in integrated photonics: From optical isolation to 4D quantum Hall physics
• Circuit Implementation of a Four-Dimensional Topological Insulator
• Experimental band structure spectroscopy along a synthetic dimension
• Higher-order topological insulators in synthetic dimensions
• Realizing Su-Schrieffer-Heeger topological edge states in Rydberg-atom synthetic dimensions
• Synthetic space with arbitrary dimensions in a few rings undergoing dynamic modulation
• Ferromagnetic hybrid nodal loop and switchable type-I and type-II Weyl fermions in two-dimension
• Tutorial: synthetic frequency dimensions in dynamically modulated ring resonators
• Mode-Locked Topological Insulator Laser Utilizing Synthetic Dimensions
• Topological phases in ring resonators: recent progress and future prospects
• Quantum simulation of non-trivial topology
• A comprehensive review on developments of synthetic dimensions
• Multidimensional synthetic chiral-tube lattices via nonlinear frequency conversion
• Three-dimensional Chiral Lattice Fermion in Floquet Systems
• Theory of a 3+1D fractional chiral metal: interacting variant of the Weyl semimetal
• Creating locally interacting Hamiltonians in the synthetic frequency dimension for photons
• Setting Boundaries with Memory: Generation of Topological Boundary States in Floquet-Induced Synthetic Crystals
• Topological holographic quench dynamics in a synthetic dimension
• Many-body quantum interference on hypercubes
• Bose-Hubbard physics in synthetic dimensions from interaction Trotterization
• Four-dimensional topological lattices through connectivity
• Observation of flat-band and band transition in the synthetic space
• Extreme defect sensitivity from large synthetic dimensionality
• Exceptional Cones in 4D Parameter Space
• Electric fields for light: Propagation of microwave photons along a synthetic dimension
• Multi-Photon Synthetic Lattices in Multi-Port Waveguide Arrays: Synthetic Atoms and Fock Graphs
• The Harper-Hofstadter Hamiltonian and conical diffraction in photonic lattices with grating assisted tunneling
• Observation of gapless corner modes in synthetic translation dimensions
• Building Flat-Band Lattice Models from Gram Matrices
• Synthetic dimensions and topological chiral currents in mesoscopic rings
• Onset of pseudogap and density wave in a system with a closed Fermi surface
• Four-dimensional Floquet topological insulator with an emergent second Chern number
• Quasi-edge states and topological Bloch oscillation in the synthetic space
• Creating high-dimensional topological physics using a single ring resonator
• Topological characteristics of gap closing points in nonlinear Weyl semimetals