Topological Phase Transitions and Thouless Pumping of Light in Photonic Waveguide Arrays
arXiv:1603.01044 · doi:10.1002/lpor.201600119
Abstract
Photonic waveguide arrays provide an excellent platform for simulating conventional topological systems, and they can also be employed for the study of novel topological phases in photonics systems. However, a direct measurement of bulk topological invariants remains a great challenge. Here we study topological features of generalized commensurate Aubry-André-Harper (AAH) photonic waveguide arrays and construct a topological phase diagram by calculating all bulk Chern numbers, and then explore the bulk-edge correspondence by analyzing the topological edge states and their winding numbers. In contrast to incommensurate AAH models, diagonal and off-diagonal commensurate AAH models are not topologically equivalent. In particular, there appear nontrivial topological phases with large Chern numbers and topological phase transitions. By implementing Thouless pumping of light in photonic waveguide arrays, we propose a simple scheme to measure the bulk Chern numbers.
accepted for publication in Laser & Photonics Reviews
References in corpus (39)
- Berry Phase Effects on Electronic Properties
- Maximally-localized generalized Wannier functions for composite energy bands
- Topological Photonics
- Photonic Floquet Topological Insulators
- Maximally localized Wannier functions: Theory and applications
- Imaging topological edge states in silicon photonics
- Robust optical delay lines via topological protection
- Chern Numbers in Discretized Brillouin Zone: Efficient Method of Computing (Spin) Hall Conductances
- Topological States and Adiabatic Pumping in Quasicrystals
- Direct Measurement of the Zak phase in Topological Bloch Bands
- Solitons in nonlinear lattices
- Measuring the Chern number of Hofstadter bands with ultracold bosonic atoms
- Quantum spin Hall effect of light
- Towards Quantum Chemistry on a Quantum Computer
- Probing topological invariants in the bulk of a non-Hermitian optical system
- A Thouless Quantum Pump with Ultracold Bosonic Atoms in an Optical Superlattice
- Topological Thouless Pumping of Ultracold Fermions
- Topological Anderson Insulator
- Observation of dynamic localization in periodically-curved waveguide arrays
- Experimental Observation of Large Chern numbers in Photonic Crystals
- Edge states and topological phases in one-dimensional optical superlattices
- Topological Zero-Energy Modes in Gapless Commensurate Aubry-André-Harper Models
- Topological Equivalence between the Fibonacci Quasicrystal and the Harper Model
- Matter-wave gap solitons in atomic bandgap structures
- Scattering theory of topological insulators and superconductors
- Measurement of topological invariants in a 2D photonic system
- Quantum simulation of the wavefunction to probe frustrated Heisenberg spin systems
- Localization and adiabatic pumping in a generalized Aubry-André-Harper model
- Inhibition of light tunneling in waveguide arrays
- Geometrical pumping with a Bose-Einstein condensate
- Implementation of Quantum and Classical Discrete Fractional Fourier Transforms
- Anomalous and Quantum Hall Effects in Lossy Photonic Lattices
- Topological Bose-Mott Insulators in a One-Dimensional Optical Superlattice
- Measuring topological invariants in photonic systems
- Simulation and Detection of Photonic Chern Insulators in One-Dimensional Circuit Quantum Electrodynamics Lattice
- A photonic thermalization gap in disordered lattices
- Topological classification of adiabatic processes
- Phase spectroscopy of topological invariants in photonic crystals
- Seeing bulk topological properties of band insulators in small photonic lattices
Cited by in corpus (58)
- Topological Photonics
- Thouless pumping and topology
- Quantized Nonlinear Thouless Pumping
- Observation of anomalous π modes in photonic Floquet engineering
- Experimental observation of non-Abelian topological charges and bulk-edge correspondence
- Edge states in trimer lattices
- Quantized Fractional Thouless Pumping of Solitons
- Observation of Non-Abelian Thouless Pump
- Multi-particle Wannier states and Thouless pumping of interacting bosons
- The Chern Number Governs Soliton Motion in Nonlinear Thouless Pumps
- Dynamic winding number for exploring band topology
- Topological quantum transport and spatial entanglement distribution via disordered bulk channel
- Interactions enable Thouless pumping in a nonsliding lattice
- Spontaneous topological pumping in non-Hermitian systems
- Non-diffracting states in one-dimensional Floquet photonic topological insulators
- Liquid-crystal-based topological photonics
- Quantized Topological Anderson-Thouless Pump
- Creation and annihilation of mobile fractional solitons in atomic chains
- Topological Phase Transition and Charge Pumping in a One-Dimensional Periodically Driven Optical Lattice
- Topological Floquet edge states in periodically curved waveguides
- Analytical solution of open crystalline linear 1D tight-binding models
- Dispersion Suppressed Topological Thouless Pumping
- Topological pumping assisted by Bloch oscillations
- Thouless pumping in a driven-dissipative Kerr resonator array
- Probing topological phases in waveguide superlattices
- Topological phase transitions of Thouless charge pumping realized in helical organic molecules with long-range hoppings
- Nonlinear Thouless Pumping of Solitons Across an Impurity
- Phonon-induced breakdown of Thouless pumping in the Rice-Mele-Holstein model
- Direct measurement of topological invariants through temporal adiabatic evolution of bulk states in the synthetic Brillouin zone
- Symmetry-Protected Quantum Adiabatic Evolution in Spontaneous Symmetry-Breaking Transitions
- Nonlinearity-induced Fractional Thouless Pumping of Solitons
- Transport of Vector Solitons in Spin-Dependent Nonlinear Thouless Pumps
- Biorthogonal topological charge pumping in non-Hermitian systems
- Realization of programmable nanomechanical lattice with both nearest-neighboring and next-nearest-neighboring couplings
- Nonparaxiality-triggered Landau-Zener transition in topological photonic waveguides
- Topological pumping induced by spatiotemporal modulation of interaction
- Topological photon pumping in quantum optical systems
- Nonadiabatic nonlinear non-Hermitian quantized pumping
- Uncover band topology via quantized drift in two-dimensional Bloch oscillations
- Topological characteristics of gap closing points in nonlinear Weyl semimetals
- Generalized Aubry-Andre-Harper Models in Optical Superlattices
- Symmetry-protected Landau-Zener-Stückelberg-Majorana interference and non-adiabatic topological transport of edge states
- Floquet defect solitons
- Asymmetric topological pumping in nonparaxial photonics
- Exploring Thouless Pumping in the Generalized Creutz Model: A Graphical Method and Modulation Schemes
- Floquet-Anderson localization in the Thouless pump and how to avoid it
- Absence of disordered Thouless pumps at finite frequency
- Observation of Square-Root Higher-Order Topological States in Photonic Waveguide Arrays
- A spectrum-based shortcut method for topological systems
- Tunable zero modes and quantum interferences in flat-band topological insulators
- Constructing qubit edge states by inverse-designing the electromagnetic environment
- Zak Phase Dislocations in Trimer Lattices
- Survival of Hermitian Criticality in the Non-Hermitian Framework
- Families of Skyrmions in Two-Dimensional Spin-1/2 Systems
- Topological Unwinding in an Exciton-Polariton Condensate Array
- Topological dynamics of adiabatic cat states
- Realizing Topological Quantum Walks on NISQ Digital Quantum Computer
- Topological power pumping in quantum circuits