Interacting bosons in generalized zig-zag and railroad-trestle models

We theoretically study the ground-state phase diagram of strongly interacting bosons on a generalized zig-zag ladder model, the rail-road trestle (RRT) model. By means of analytical arguments in the limits of decoupled chains and the case of vanishing fillings as well as extensive DMRG calculations we examine the rich interplay between frustration and interaction for various parameter regimes. We distinguish three different cases, the fully frustrated RRT model where the dispersion relation becomes doubly degenerate and an extensive chiral superfluid regime is found, the anti-symmetric RRT with alternating $\pi$ and $0$ fluxes through the ladder plaquettes and the sawtooth limit, which is closely related to the latter case. We study detailed phase diagrams which include besides different single component superfluids, the chiral superfluid phases, the two component superfluids and different gaped phases, with dimer and a charge-density wave order.Comment: 10 pages, 16 figure

The Anyon Hubbard Model in One-Dimensional Optical Lattices

Raman-assisted hopping may be used to realize the anyon Hubbard model in one-dimensional optical lattices. We propose a feasible scenario that significantly improves the proposal of [T. Keilmann et al., Nature Commun. 2, 361 (2011)], allowing as well for an exact realization of the two-body hard-core constraint, and for controllable effective interactions without the need of Feshbach resonances. We show that the combination of anyonic statistics and two-body hard-core constraint leads to a rich ground state physics, including Mott insulators with attractive interactions, pair superfluids, dimer phases, and multicritical points. Moreover, the anyonic statistics results in a novel two-component superfluid of holon and doublon dimers, characterized by a large but finite compressibility and a multipeaked momentum distribution, which may be easily revealed experimentally.Comment: 5 pages, 4 figure

Probing the exchange statistics of one-dimensional anyon models

We propose feasible scenarios for revealing the modified exchange statistics in one-dimensional anyon models in optical lattices based on an extension of the multicolor lattice-depth modulation scheme introduced in [{Phys. Rev. A 94, 023615 (2016)}]. We show that the fast modulation of a two-component fermionic lattice gas in the presence a magnetic field gradient, in combination with additional resonant microwave fields, allows for the quantum simulation of hardcore anyon models with periodic boundary conditions. Such a semi-synthetic ring set-up allows for realizing an interferometric arrangement sensitive to the anyonic statistics. Moreover, we show as well that simple expansion experiments may reveal the formation of anomalously bound pairs resulting from the anyonic exchange.Comment: 8 pages, 9 figure

Anomalous pairing of bosons: Effect of multi body interactions in optical lattice

An interesting first order type phase transition between Mott lobes has been reported in Phys. Rev. Lett. 109, 135302 (2012) for a two-dimensional Bose-Hubbard model in the presence of attractive three-body interaction. We re-visit the scenario in a system of ultracold bosons in a one-dimensional optical lattice using the density matrix renormalization group method and show that an unconventional pairing of particles occurs due to the competing two-body repulsive and three-body attractive interactions. This leads to a pair superfluid phase sandwiched between the Mott insulator lobes corresponding to densities $\rho=1$ and $\rho=3$ in the strongly interacting regime. We further extend our analysis to a two dimensional Bose-Hubbard model using the self consistent cluster-mean-field theory approach and confirm that the unconventional pair superfluid phase stabilizes in the region between the Mott lobes in contrast to the direct first order jump as predicted before. In the end we establish connection to the most general Bose-Hubbard model and analyse the fate of the pair superfluid phase in presence of an external trapping potential.Comment: 5 pages, 6 figure

Polar molecules in frustrated triangular ladders

Polar molecules in geometrically frustrated lattices may result in a very rich landscape of quantum phases, due to the non-trivial interplay between frustration, and two- and possibly three-body inter-site interactions. In this paper, we illustrate this intriguing physics for the case of hard-core polar molecules in frustrated triangular ladders. Whereas commensurate lattice fillings result in gapped phases with bond-order and/or density-wave order, at incommensurate fillings we find chiral-, two-component-, and pair-superfluids. We show as well that, remarkably, polar molecules in frustrated lattices allow, for the first time to our knowledge, for the observation of bond-ordered supersolids

Exploring Unconventional Hubbard Models with Doubly Modulated Lattice Gases

Recent experiments show that periodic modulations of cold atoms in optical lattices may be used to engineer and explore interesting models. We show that double modulation, combining lattice shaking and modulated interactions allows for the engineering of a much broader class of lattice models with correlated hopping, which we study for the particular case of one-dimensional systems. We show, in particular, that by using this double modulation it is possible to study Hubbard models with asymmetric hopping, which, contrary to the standard Hubbard model, present insulating phases with both parity and string order. Moreover, double modulation allows for the simulation of lattice models in unconventional parameter regimes, as we illustrate for the case of the spin-$1/2$ Fermi-Hubbard model with correlated hopping, a relevant model for cuprate superconductors.Comment: 5 pages, 3 figure

Universal Hall Response in Synthetic Dimensions

We theoretically study the Hall effect on interacting $M$-leg ladder systems, comparing different measures and properties of the zero temperature Hall response in the limit of weak magnetic fields. Focusing on $SU(M)$ symmetric interacting bosons and fermions, as relevant for e.g. typical synthetic dimensional quantum gas experiments, we identify an extensive regime in which the Hall imbalance $\Delta_{\rm H}$ is universal and corresponds to a classical Hall resistivity $R_{\rm H}=-1/n$ for a large class of quantum phases. Away from this high symmetry point we observe interaction driven phenomena such as sign reversal and divergence of the Hall response.Comment: 13 pages, 9 figure

Three-body constrained bosons in double-well optical lattice

We analyse the ground-state properties of three-body constrained bosons in a one dimensional optical lattice with staggered hoppings analogous to the double well optical lattice. By considering attractive and repulsive on-site interactions between the bosons, we obtain the phase diagram which exhibits various quantum phases. Due to the double-well geometry and three-body constraint several gapped phases such as the Mott insulators and dimer/bond-order phases emerge at commensurate densities in the repulsive interaction regime. Attractive interaction leads to the pair formation which leads to the pair bond order phase at unit filling which resembles the valence-bond solid phase of composite bosonic pairs. At incommensurate densities we see the signatures of the gapless pair superfluid phase.Comment: 10 pages, 19 figure

Supersolid and pair correlations of the extended Jaynes-Cummings-Hubbard model on triangular lattices

We study the extended Jaynes-Cummings-Hubbard model on triangular cavity lattices and zigzag ladders. By using density-matrix renormalization group methods, we observe various types of solids with different density patterns and find evidence for light supersolids, which exist in extended regions of the phase diagram of the zigzag ladder. Furthermore, we observe strong pair correlations in the supersolid phase due to the interplay between the atoms in the cavities and atom-photon interaction. By means of cluster mean-field simulations and a scaling of the cluster size extending our analysis to two-dimensional triangular lattices, we present evidence for the emergence of a light supersolid in this case also.Comment: 11 pages, 16 figure

Density-dependent synthetic magnetism for ultracold atoms in optical lattices

Raman-assisted hopping can allow for the creation of density-dependent synthetic magnetism for cold neutral gases in optical lattices. We show that the density-dependent fields lead to a non-trivial interplay between density modulations and chirality. This interplay results in a rich physics for atoms in two-leg ladders, characterized by a density-driven Meissner- to vortex-superfluid transition, and a non-trivial dependence of the density imbalance between the legs. Density-dependent fields also lead to intriguing physics in square lattices. In particular, it leads to a density-driven transition between a non-chiral and a chiral superfluid, both characterized by non-trivial charge density-wave amplitude. We finally show how the physics due to the density-dependent fields may be easily probed in experiments by monitoring the expansion of doublons and holes in a Mott insulator, which presents a remarkable dependence on quantum fluctuations.Comment: 5 pages, 4 figure