Fractional Chern insulators are the proposed phases of matter mimicking the physics of fractional quantum Hall states on a lattice without an overall magnetic field. The notion of Floquet fractional Chern insulators refers to the potential possibilities to generate the underlying topological bandstructure by means of Floquet engineering. In these schemes, a highly controllable and strongly interacting system is periodically driven by an external force at a frequency such that double tunneling events during one forcing period become important and contribute to shaping the required effective energy bands. We show that in the described circumstances it is necessary to take into account also third order processes combining two tunneling events with interactions. Referring to the obtained contributions as micromotion-induced interactions, we find that those interactions tend to have a negative impact on the stability of fractional Chern insulating phases and discuss implications for future experiments.
We propose a procedure to achieve a complete energy conversion between laser pulses carrying orbital angular momentum (OAM) in a cloud of cold atoms characterized by a double-Λ atom-light coupling scheme. A pair of resonant spatially dependent control fields prepare atoms in a positiondependent coherent population trapping state, while a pair of much weaker vortex probe beams propagate in the coherently driven atomic medium. Using the adiabatic approximation we derive the propagation equations for the probe beams. We consider a situation where the second control field is absent at the entrance to the atomic cloud and the first control field goes to zero at the end of the atomic medium. In that case the incident vortex probe beam can transfer its OAM to a generated probe beam. We show that the efficiency of such an energy conversion approaches the unity under the adiabatic condition. On the other hand, by using spatially independent profiles of the control fields, the maximum conversion efficiency is only 1/2.
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
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