Dynamics in bosonic lattice systems

The experimental realization of Harper-Hofstadter model in ultracold atomic gases has placed the study of dynamical properties of interacting bosonic lattice systems within reach. How to prepare and identify a nontrivial state becomes the main question now. In the first part, I will talk about our work on the dynamical properties of a fractional Chern insulator state, which is expected to emerge for sufficiently strong interactions when half-filling the lowest band. We explore, using density matrix renormalization group simulations, the response of the FCI state to spatially localized perturbations. After confirming the static properties of the phase we show that the characteristic, gapless features are clearly visible in the edge dynamics. We find that a local edge perturbation in this model propagates chirally independent of the perturbation strength. This contrasts the behavior of single-particle models with counter-propagating edge states, such as the noninteracting Harper-Hofstadter model, where the chirality is manifest only for weak perturbations. Additionally, our simulations show that there is inevitable density leakage from the first row of sites into the bulk, preventing a naive chiral Luttinger theory interpretation of the dynamics. In the second part, I will discuss different protocols to prepare a state through adiabatic time evolution and will focus on our work about preparing a state in a two-leg ladder, where a homogeneous artificial magnetic field is switched on linearly by ramping up the corresponding artificial vector potentials (i.e. the Peierls phases). Using simulations based on the density matrix renormalization group, we find that the efficiency of adiabatic preparation depends dramatically on the choice of the Peierls phases. This effect is explained by the fact that, during the ramp, this choice is not simply a choice of gauge, since the time derivative of the Peierls phases corresponds to artificial electric fields. Remarkably, we find that for an optimal choice, these induced electric fields allow for preparing the ground state almost instantaneously. This provides a novel concept for robust state preparation and shortcuts to adiabaticity.