Understanding the robustness of topological phases of matter in the presence of strong interactions, and synthesising novel strongly-correlated topological materials, lie among the most important and difficult challenges of modern theoretical and experimental physics. In this work, we present a complete theoretical analysis of the synthetic Creutz-Hubbard ladder, which is a paradigmatic model that provides a neat playground to address these challenges. We put special attention to the competition of correlated topological phases and orbital quantum magnetism in the regime of strong interactions. These results are furthermore confirmed and extended by extensive numerical simulations. Moreover we propose how to experimentally realize this model in a synthetic ladder, made of two internal states of ultracold fermionic atoms in a one-dimensional optical lattice. Our work paves the way towards quantum simulators of interacting topological insulators with cold atoms.Contents arXiv:1612.02996v2 [cond-mat.quant-gas]

We show that ultracold Fermi gases in optical superlattices can be used as quantum simulators of relativistic lattice fermions in 3+1 dimensions. By exploiting laser-assisted tunneling, we find an analogue of the so-called naive Dirac fermions, and thus provide a realization of the fermion doubling problem. Moreover, we show how to implement Wilson fermions, and discuss how their mass can be inverted by tuning the laser intensities. In this regime, our atomic gas corresponds to a phase of matter where Maxwell electrodynamics is replaced by axion electrodynamics: a 3D topological insulator.

Spinor Bose condensates loaded in optical lattices have a rich phase diagram characterized by different magnetic order. Here we apply the density matrix renormalization group to accurately determine the phase diagram for spin-1 bosons loaded on a one-dimensional lattice. The Mott lobes present an even or odd asymmetry associated to the boson filling. We show that for odd fillings the insulating phase is always in a dimerized state. The results obtained in this work are also relevant for the determination of the ground state phase diagram of the S = 1 Heisenberg model with biquadratic interaction.

We study persistent currents for interacting one-dimensional bosons on a tight ring trap, subjected to a rotating barrier potential, which induces an artificial U (1) gauge field. We show that, at intermediate interactions, the persistent current response is maximal, due to a subtle interplay of effects due to the barrier, the interaction and quantum fluctuations. These results are relevant for ongoing experiments with ultracold atomic gases on mesoscopic rings. 03.75.Lm, 71.10.Pm, 73.23.Ra A quantum fluid confined on a ring and subjected to a U (1) gauge potential displays a periodicity in the particle current as a function of the flux of the corresponding classical gauge field. This persistent current phenomenon is a manifestation of the Aharonov-Bohm effect, and reflects the macroscopic coherence of the manybody wave function along the ring. Such currents were observed more than 50 years ago in bulk superconductors [1] and, more recently, in normal metallic rings, overcoming the challenges of the decoherence induced by inelastic scattering [2]. The most recent developments in the manipulation of ultracold atoms on ring traps [3, 4] have disclosed a novel platform for the study of persistent currents, which can be induced by the application of a rotating localized barrier or, alternatively, by inducing suitable artificial gauge fields [5]. Tunable localized barriers in toroidal Bose-Einstein condensates have been realized, using well-focused, repulsively tuned laser beams [4]. Also, recently the engineering of an atomic superconducting quantum interference device was demonstrated [6]. The unprecedented variety of interaction and barrier strength regimes paves the way to applications such as high-precision measurements, atom interferometry and quantum information, e.g., by the construction of macroscopic superposition of current states and flux qubits [7][8][9].The scenario becomes particularly intriguing if the transverse section of the ring is sufficiently thin to effectively confine the system in one dimension (1D): the rich interplay between interactions, quantum fluctuations, and statistics acquires a role of primary relevance. In absence of any obstacle along the ring, the persistent currents display an ideal sawtooth behavior as a function of the flux, i.e., perfect superfluidity for any interaction strength at zero temperature [10, 11]. Diamagnetic or paramagnetic response depending on the population parity is expected [12] for fermions but not for bosons. If a localized barrier is added, persistent currents are smeared-their shape taking a sinusoidal form in the case of large-barrier or small-tunneling limit-as obtained for thin superconducting rings from a Luttinger-liquid approach [13]. Beyond these limiting regimes the physics of bosonic persistent current remains unexplored.The aim of the present work is to provide a complete characterization of persistent currents for 1D bosons, in all interaction and barrier strength regimes. By combining analytical as well as numerical techniques suited fo...

We present a proposal for a versatile cold-atom-based quantum simulator of relativistic fermionic theories and topological insulators in arbitrary dimensions. The setup consists of a spin-independent optical lattice that traps a collection of hyperfine states of the same alkaline atom, to which the different degrees of freedom of the field theory to be simulated are then mapped. We show that the combination of bi-chromatic optical lattices with Raman transitions can allow the engineering of a spin-dependent tunneling of the atoms between neighboring lattice sites. These assisted-hopping processes can be employed for the quantum simulation of various interesting models, ranging from noninteracting relativistic fermionic theories to topological insulators. We present a toolbox for the realization of different types of relativistic lattice fermions, which can then be exploited to synthesize a majority of phases in the periodic table of topological insulators.