Setting Boundaries with Memory: Generation of Topological Boundary States in Floquet-Induced Synthetic Crystals

Abstract

When a d-dimensional quantum system is subjected to a periodic drive, it may be treated as a (d+1)-dimensional system, where the extra dimension is a synthetic one. In this work, we take these ideas to the next level by showing that non-uniform potentials, and particularly edges, in the synthetic dimension are created whenever the dynamics of system has a memory component. We demonstrate that topological states appear on the edges of these synthetic dimensions and can be used as a basis for a wave packet construction. Such systems may act as an optical isolator which allows transmission of light in a directional way. We supplement our ideas by an example of a physical system that shows this type of physics.

7 Pages, 5 Figures

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Cited by in corpus (22)

• Synthetic Dimension in Photonics
• Topological quantum matter in synthetic dimensions
• Tutorial: synthetic frequency dimensions in dynamically modulated ring resonators
• Creating boundaries along a synthetic frequency dimension
• Nonreciprocal transport based on cavity Floquet modes in optomechanics
• Deterministic photonic quantum computation in a synthetic time dimension
• A comprehensive review on developments of synthetic dimensions
• Half-integer quantized topological response in quasiperiodically driven quantum systems
• Topological two-dimensional Floquet lattice on a single superconducting qubit
• Time reflection and refraction in synthetic frequency dimension
• Creating locally interacting Hamiltonians in the synthetic frequency dimension for photons
• Floquet engineering correlated materials with unpolarized light
• Localized dynamics following a quantum quench in a non-integrable system: An example on the sawtooth ladder
• Polarization as a tuning parameter for Floquet engineering: magnetism in the honeycomb, square, and triangular Mott insulators
• Superfluid Vortices in Four Spatial Dimensions
• Flow Equations for Disordered Floquet Systems
• Quantized topological phases beyond square lattices in Floquet synthetic dimensions
• Curved vortex surfaces in four-dimensional superfluids: II. Equal-frequency double rotations
• Curved vortex surfaces in four-dimensional superfluids: I. Unequal-frequency double rotations
• Quantized frequency-domain polarization of driven phases of matter
• Liouville Fock state lattices and potential simulators
• Quantized Chern-Simons Axion Coupling in Anomalous Floquet Systems