Numerically Shaking Bosonic Condensates: Successes and Breakdowns of Floquet-Band Engineering

Here we numerically study homogeneous Bose condensates subjected to a periodically driven lattice, as was performed in recent experiments [1,2]. Making no assumptions about Floquet bandstructure, we show where and when lattice shaking leads to the domain formation anticipated by the Floquet picture. This occurs abruptly at a critical shaking amplitude and is consistent with a (dynamical) quantum critical phase transition. In the weak interaction limit, for fast and slow ramp rates, we find that the transition is second order and we present clear evidence for Kibble-Zurek scaling. Detailed comparison with recent experiments shows very good agreement [1,2]. [1] C. V. Parker, L.-C. Ha, C. Chin Nat. Phys. 9, 769-774 (2013) [2] L. W. Clark, L. Feng, C. Chin, Science 354, 6312 (2016)