We report on the experimental realization of a uniform synthetic magnetic flux and the observation of Aharonov-Bohm cages in photonic lattices. Considering a rhombic array of optical waveguides, we engineer modulation-assisted tunneling processes that effectively produce nonzero magnetic flux per plaquette. This synthetic magnetic field for light can be tuned at will by varying the phase of the modulation. In the regime where half a flux quantum is realized in each plaquette, all the energy bands dramatically collapse into nondispersive (flat) bands and all eigenstates are completely localized. We demonstrate this Aharonov-Bohm caging by studying the propagation of light in the bulk of the photonic lattice. Besides, we explore the dynamics on the edge of the lattice and discuss how the corresponding edge states can be continuously connected to the topological edge states of the Creutz ladder. Our photonic lattice constitutes an appealing platform where the interplay between engineered gauge fields, frustration, localization, and topological properties can be finely studied.

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We consider two interacting bosons in a dimerized Su-Schrieffer-Heeger (SSH) lattice. We identify a rich variety of two-body states. In particular, for open boundary conditions and moderate interactions, edge bound states (EBS) are present even for the dimerization that does not sustain single-particle edge states. Moreover, for large values of the interactions, we find a breaking of the standard bulk-boundary correspondence. Based on the mapping of two interacting particles in one dimension onto a single particle in two dimensions, we propose an experimentally realistic coupled optical fibers setup as quantum simulator of the two-body SSH model. This setup is able to highlight the localization properties of the states as well as the presence of a resonant scattering mechanism provided by a bound state that crosses the scattering continuum, revealing the closed-channel population in real time and real space.Comment: 14 pages; 14 figure

By using a modulated magnetic field in a Feshbach resonance for ultracold fermionic atoms in optical lattices, we show that it is possible to engineer a class of models usually referred to as correlated-hopping models. These models differ from the Hubbard model in exhibiting additional density-dependent interaction terms that affect the hopping processes. In addition to the spin-SU(2) symmetry, they also possess a charge-SU(2) symmetry, which opens the possibility of investigating the η-pairing mechanism for superconductivity introduced by Yang for the Hubbard model. We discuss the known solution of the model in one dimension (where η states have been found in the degenerate manifold of the ground state) and show that, away from the integrable point, quantum Monte Carlo simulations at half filling predict the emergence of a phase with coexisting incommensurate spin and charge order.

Topological states of matter are peculiar quantum phases showing different edge and bulk transport properties connected by the bulk-boundary correspondence. While non-interacting fermionic topological insulators are well established by now and have been classified according to a ten-fold scheme, the possible realisation of topological states for bosons has not been much explored yet. Furthermore, the role of interactions is far from being understood. Here, we show that a topological state of matter exclusively driven by interactions may occur in the p-band of a Lieb optical lattice filled with ultracold bosons. The single-particle spectrum of the system displays a remarkable parabolic band-touching point, with both bands exhibiting non-negative curvature. Although the system is neither topological at the single-particle level, nor for the interacting ground state, on-site interactions induce an anomalous Hall effect for the excitations, carrying a non-zero Chern number. Our work introduces an experimentally realistic strategy for the formation of interaction-driven topological states of bosons.Introduction. The seminal work of Kane and Mele for graphene in the presence of a strong spin-orbit coupling [1] has opened the field of topological insulators and brought us a deeper comprehension of phenomena like the quantum Hall effect, which had been known for decades [2]. A universal classification scheme based on symmetries and dimensionality has enabled a solid basis for our understanding of non-interacting fermionic topological systems [3][4][5][6]. In contrast, interaction-driven topological states of matter have remained elusive. Topological phases were originally predicted to occur in lattice models with dominating next-nearest-neighbor interaction [7], a scenario which appears difficult to envisage in real experiments. More precise exact diagonalization [8] and DMRG [9] calculations, however, contradicted these mean-field results.Predictions of topological phases in Dirac-like materials exhibiting a linear dispersion suffer from the additional drawback that theses systems are genuinely quantum critical: due to the zero density of states at the neutrality point, only perturbations exceeding a certain critical value are able to induce a topological phase. On the other hand, systems with a parabolic band touching point may become topological for infinitesimal values of the interaction [10]. A paradigmatic example is Bernalstacked bilayer graphene [11], but other cases have also been identified, and this field has attracted much interest recently [12,13].The search for interaction-driven topological systems has mostly concentrated on electronic condensed matter [7-10, 13, 14] or on the equivalent cold-atom fermion system [12,15,16]. Only recently, the corresponding bosonic analogs became the subject of theoretical investigations [17][18][19][20][21]. As for experiments, considerable progress has been achieved in realizing topologi-