Topology and interactions in the photonic Creutz and Creutz-Hubbard ladders

Abstract

The latest advances in the field of photonics have enabled the simulation of an increasing number of quantum models in photonic systems, turning them into an important tool for realizing exotic quantum phenomena. In this paper we suggest different ways in which these systems can be used to study the interplay between flat band dynamics, topology and interactions in a well-known quasi-1D topological insulator: the Creutz ladder. Firstly, a simple experimental protocol is proposed to observe the Aharonov-Bohm localization in the noninteracting system, and the different experimental setups that might be used for this are reviewed. We then consider the inclusion of a repulsive Hubbard-type interaction term, which can give rise to repulsively bound pairs termed doublons. The dynamics of these quasiparticles are studied for different points of the phase diagram, including a regime in which pairs are localized and particles are free to move. Finally, a scheme for the photonic implementation of a two-particle bosonic Creutz-Hubbard model is presented.

arXiv commentV2: Minor changes in response to referee comments

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• Interaction-induced topological properties of two bosons in flat-band systems
• Extended flat-bands, entanglement and topological properties in a Creutz ladder
• Topological properties of subsystem-symmetry-protected edge states in an extended quasi-one-dimensional dimerized lattice
• Interaction induced doublons and embedded topological subspace in a complete flat-band system
• Non-thermalized Dynamics of Flat-Band Many-Body Localization
• Floquet topological phases with fourfold-degenerate edge modes in a driven spin-1/2 Creutz ladder
• Interaction-induced topological states of photon pairs
• Observation of inverse Anderson transitions in Aharonov-Bohm topolectrical circuits
• Fast quantum transfer mediated by topological domain walls
• Observation of flat-band localization and topological edge states induced by effective strong interactions in electrical circuit networks
• Interplay and competition between disorder and flat band in an interacting Creutz ladder
• Non-Hermitian Floquet phases with even-integer topological invariants in a periodically quenched two-leg ladder
• Many-body Aharonov-Bohm caging in a lattice of rings
• Edge mode manipulation through commensurate multifrequency driving
• Tailoring flat bands and topological phases in a multi-strand Creutz network
• Topological inverse Anderson insulator
• Doublons, topology and interactions in a one-dimensional lattice
• Exact projector Hamiltonian, local integrals of motion, and many-body localization with topological order
• Ubiquity of the quantum boomerang effect in Hermitian Anderson-localized systems
• Cataloging topological phases of $N$-stacked Su-Schrieffer-Heeger chains by a systematic breaking of symmetries
• Electric circuit emulation of topological transitions driven by quantum statistics
• Topological chiral currents in the Gross-Neveu model extension
• Enhanced repulsively bound atom pairs in topological optical lattice ladders
• Quantum information spreading in random spin chains with topological order
• Topological properties of a periodically driven Creutz ladder
• Flat Bands and Compact Localised States: A Carrollian roadmap
• Higher-order topological phase of interacting photon pairs
• Tunable Aharonov-Bohm cages through anti-$\mathcal{P}\mathcal{T}$-symmetric imaginary couplings
• Hund's coupling-assisted ferromagnetic percolation transition in a multiorbital flat band
• Topological two-body bands in a multiband Hubbard model
• Unconventional edge states in a two-leg ladder
• Superfluidity from correlations in driven boson systems
• Flat-band engineering of quasi-one-dimensional systems via supersymmetric transformations
• Deformation of localized states and state transitions in systems of randomly hopping interacting fermions
• Flat-band full localization and symmetry-protected topological phase on bilayer lattice systems
• Multipartite entanglement distribution in a topological photonic network
• Exploring Thouless Pumping in the Generalized Creutz Model: A Graphical Method and Modulation Schemes
• Localization and slow-thermalization in a cluster spin model
• Chern numbers for the two-body Hofstadter-Hubbard butterfly
• Tunable zero modes and quantum interferences in flat-band topological insulators
• Probing the topology of the two-photon bands via time-dependent quantum walks
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• Fate of chiral order and impurity self-pinning in flat bands with local symmetry
• Higher order topology in a Creutz ladder
• Emergent topological phases in an extended Su-Schrieffer-Heeger model with Rashba spin-orbit interaction, higher order hopping and domain wall
• Synchronized Aharonov-Bohm Motifs via Engineered Dissipation
• Topological bound states in a lattice of rings with nearest-neighbour interactions