Modified interactions in a Floquet topological system on a square lattice and their impact on a bosonic fractional Chern insulator state

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 $\pm 1$, is opened in a way characteristic to 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.Comment: 10 pages, 4 figures, submitted to Physical Review

Semi-synthetic zigzag optical lattice for ultracold bosons

We consider a one-dimensional "zigzag" lattice, pictured as a two-site wide single strip taken from a triangular lattice, affected by a tunable homogeneous magnetic flux piercing its triangular plaquettes. We focus on a semi-synthetic lattice produced by combining a one-dimensional spin-dependent lattice in the long direction with laser-induced transitions between atomic internal states that define the short synthetic dimension. In contrast to previous studies on semi-synthetic lattices, the atom-atom interactions are nonlocal in both lattice directions. We investigate the ground-state properties of the system for the case of strongly interacting bosons, and find that the interplay between the frustration induced by the magnetic field and the interactions gives rise to an exotic gapped phase at fractional filling factors corresponding to one particle per magnetic unit cell.Comment: 9 pages, 6 figures; v3: final version to appear in PR

Fractionally charged excitations in a restricted-geometry lattice

The discovery of fractional quantum Hall effect (FQHE) in 2D electron gas gave rise to immense interest in topological phases of matter. One of the most intriguing features of FQHE state is fractionally charged excitations which embodies anyonic statistics. Even though the FQHE was first observed in GaAs-GaAlAs heterojunctions, experiments in optical lattices allow much more controllable study of many-body systems, therefore allowing regimes that are impossible to realise in semiconductor based experiments. Historically, FQHE comes from condensed matter systems, which can be characterized by a very large number of particles, as a consequence, theoretical studies were focused only on infinite or periodical Hamiltonians. Therefore, few of the unanswered questions remain: can FQHE states be realised in minuscule lattices, containing only several sites in diameter, and what additional effects would open boundaries produce? In this work we try to tackle both of these questions. Using numerical diagonalization of Harper-Hofstadter model we were able to observe localisation of fractional charge in a 9×6 square lattice with artificial magnetic flux. Unfortunately, close proximity to the lattice edges does not allow direct confirmation of fractional statistics