We propose a cold-atom realization of a zigzag ladder. The two legs of the ladder correspond to a “synthetic” dimension given by two internal (spin) states of the atoms, so that tunneling between them can be realized as a laser-assisted process. The zigzag geometry is achieved by employing a spin-dependent optical lattice with the site position depending on the internal atomic state, i.e., on the ladder’s leg. The lattice offers a possibility to tune the single-particle dispersion from a double-well to a single-minimum configuration. In contrast to previously considered semisynthetic lattices with a square geometry, the tunneling in the synthetic dimension is accompanied by spatial displacements of atoms. Therefore, the atom-atom interactions are nonlocal and act along the diagonal (semisynthetic) direction. We investigate the ground-state properties of the system for the case of strongly interacting bosons. In particular, we find that the interplay between the frustration induced by the magnetic field and the interactions gives rise to an interesting gapped phase at fractional filling factors corresponding to one particle per magnetic unit cell.

We consider ultracold atoms in a two-dimensional optical lattice of the dice geometry in a tightbinding regime. The atoms experience a laser-assisted tunneling between the nearest neighbor sites of the dice lattice accompanied by the momentum recoil. This allows one to engineer staggered synthetic magnetic fluxes over plaquettes, and thus pave a way towards the realization of topologically nontrivial band structures. In such a lattice the real-valued next-neighbor transitions are not needed to reach a topological regime. Yet, such transitions can increase a variety of the obtained topological phases. The dice lattice represents a triangular Bravais lattice with a three-site basis consisting of a hub site connected to two rim sites. As a consequence, the dice lattice supports three energy bands. From this point of view, our model can be interpreted as a generalization of the paradigmatic Haldane model which is reproduced if one of the two rim sub-lattices is eliminated. We demonstrate that the proposed upgrade of the Haldane model creates a significant added value, including an easy access to topological semimetal phases relying only on the nearest neighbor coupling, as well as enhanced topological band structures featuring Chern numbers higher than one leading to physics beyond the usual quantum Hall effect. The numerical investigation is supported and complemented by an analytical scheme based on the study of singularities in the Berry connection. arXiv:1501.00425v2 [cond-mat.quant-gas] 22 Sep 2015

We propose a set of schemes to create and probe fractionally charged excitations of a fractional Chern insulator state in an optical lattice. This includes the creation of localized quasiparticles and quasiholes using both static local defects and the dynamical local insertion of synthetic flux quanta. Simulations of repulsively interacting bosons on a finite square lattice with experimentally relevant open boundary conditions show that already a four-particle system exhibits signatures of charge fractionalization in the quantum-Hall-like state at the filling fraction of 1/2 particle per flux quantum. This result is favorable for the prospects of adiabatic preparation of fractional Chern insulators. Our work is inspired by recent experimental breakthroughs in atomic quantum gases: the realization of strong artificial magnetic fields in optical lattices, the ability of single-site addressing in quantum gas microscopes, and the preparation of low-entropy insulating states by engineering an entropy-absorbing metallic reservoir. arXiv:1804.02002v2 [cond-mat.quant-gas]

Phasonic degrees of freedom are unique to quasiperiodic structures, and play a central role in poorly-understood properties of quasicrystals from excitation spectra to wavefunction statistics to electronic transport. However, phasons are challenging to access dynamically in the solid state due to their complex long-range character and the effects of disorder and strain. We report phasonic spectroscopy of a quantum gas in a one-dimensional quasicrystalline optical lattice. We observe that strong phasonic driving produces a nonperturbative high-harmonic plateau strikingly different from the effects of standard dipolar driving. Tuning the potential from crystalline to quasicrystalline, we identify spectroscopic signatures of quasiperiodicity and interactions and map the emergence of a multifractal energy spectrum, opening a path to direct imaging of the Hofstadter butterfly.

We propose a simple scheme for the realization of a topological quasienergy band structure with ultracold atoms in a periodically driven optical square lattice. It is based on a circular lattice shaking in the presence of a superlattice that lowers the energy on every other site. The topological band gap, which separates the two bands with Chern numbers +/-1, is opened in a way characteristic of Floquet topological insulators, namely, by terms of the effective Hamiltonian that appear in subleading order of a high-frequency expansion. These terms correspond to processes where a particle tunnels several times during one driving period. The interplay of such processes with particle interactions also gives rise to new interaction terms of several distinct types. For bosonic atoms with on-site interactions, they include nearest-neighbor density-density interactions introduced at the cost of weakened on-site repulsion as well as density-assisted tunneling. Using exact diagonalization, we investigate the impact of the individual induced interaction terms on the stability of a bosonic fractional Chern insulator state at half filling of the lowest band