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, 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—are suggested. First, 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. The inclusion of a repulsive Hubbard‐type interaction term, which can give rise to repulsively bound pairs termed doublons, is then considered. 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.

Interaction-induced topological properties of two bosons in flat-band systems

“…By mapping the subspaces of lowest-energy two-boson states into single-particle models, we show that the system has a topologically nontrivial phase. In contrast with other realizations of two-body topological states [13,[29][30][31][32][33][34][35][36][37][38][39][40][41], in this case the topological character is controlled through effective two-boson tunneling amplitudes that depend on the interaction strength. In a diamond chain with open boundaries, this topological phase is benchmarked by the presence of robust in-gap states localized at the edges, which are in turn composed of bound pairs of bosons, each occupying a localized single-particle eigenstate.…”

“…These two-body states, which are stable even for repulsive interactions due to the finite bandwidth of the singleparticle kinetic energy [9], have been observed [10][11][12][13] and extensively analyzed [14][15][16][17][18][19][20][21][22][23][24][25] in optical lattices, and have also been emulated in photonic systems [26,27] and in topolectrical circuits [28]. Motivated in part by these advances, several recent works have focused on the topological properties of two-body states [13,[29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44], with the long-term aim of paving the path to a better comprehension of topological phases in a full many-body interacting scenario. A distinctive advantage that these small-sized systems offer is that it is often possible to map the problem of two interacting particles in a lattice into a single-particle model defined in a different lattice, the topological characterization of which can then be performed with well-established techniques [31][32][33]36,40,…”

“…Motivated in part by these advances, several recent works have focused on the topological properties of two-body states [13,[29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44], with the long-term aim of paving the path to a better comprehension of topological phases in a full many-body interacting scenario. A distinctive advantage that these small-sized systems offer is that it is often possible to map the problem of two interacting particles in a lattice into a single-particle model defined in a different lattice, the topological characterization of which can then be performed with well-established techniques [31][32][33]36,40,41].…”

Non-Hermitian Floquet Phases with Even-Integer Topological Invariants in a Periodically Quenched Two-Leg Ladder

“…It could possess symmetry-protected degenerate zero modes at its boundaries, and therefore belong to one of the earliest examples of a topological insulator [ 66 ]. In later studies, the CL model has been realized in photonic [ 67 , 68 ] and cold atom [ 69 , 70 ] systems, and utilized in the investigations of Aharonov–Bohm cages [ 71 , 72 ], topological pumping [ 73 ], localization [ 74 , 75 ], and many-body topological matter [ 76 , 77 , 78 , 79 , 80 ]. Recently, spin- extensions of the CL model have also been explored in several studies [ 81 , 82 , 83 ], leading to the discoveries of richer topological features.…”

Tunable zero modes and quantum interferences in flat-band topological insulators

“…Flat-band models have attracted a great deal of research in recent years, in part because of the discovery of magic-angle twisted bilayer graphene [30]. The Creutz ladder and other quasi-1D flat-band models like the rhombus chain can serve as toy models to explore the interplay of localization dynamics with interactions or topology [7,20,21,[31][32][33]. Other studied variants of the Creutz ladder include additional Peierls phases or on-site energies [11][12][13]34], Floquet driving [35,36], spin-1/2 particles [16,35,37] or superconductivity [32,38].…”