Bose-Einstein condensation in effective Harper-Hofstadter bands: simulations of synthetic magnetic fields by optical lattice shaking

The cold atom field has been focused on generating topological and other exotic phases of quantum matter by, for example, creating strong
synthetic magnetic fields. In the present work we use time-dependent Gross-Pitaevskii simulations to investigate the feasibility of these
schemes. There are several key questions we numerically address: 1. Can one implement shaking so that a BEC will emerge, consistent with the effective energy minima of Bloch-Floquet bandstructure? 2. How realistic is it to experimentally enter the Harper-Hofstadter regime which involves extreme parameter values (such as for hopping and shaking frequency)? 3. An important attribute of applying these Bloch-Floquet recipes to cold atoms is that there are easily tunable many-body interactions present, which are necessary for equilibration. One can
then be concerned that they undermine the single-particle Floquet bandstructure. In this talk we address these issues, and in the process
provide advice for experimentalists in implementing these shaking recipes for arriving at a Hofstader BEC. Additionally, in our simulations we investigate what underlies ”heating” and how it is affected by the strength of the interactions g.