We prove the multi-band Bloch oscillation and Stark ladder in the nk and site representation from the Floquet theorem. The proof is also possible from the equivalence between the Floquet system, Bloch oscillation, and the rotator with spin. We also exactly solve the periodically driven two level atom and two band Bloch oscillation in terms of Heun function.
Cite
@article{arxiv.0711.1458,
title = {Floquet system, Bloch oscillation, and Stark ladder},
author = {Tao Ma and Shu-Min Li},
journal= {arXiv preprint arXiv:0711.1458},
year = {2007}
}