“…Although these phenomena could be observed in systems where Bloch oscillations have been realized, such as optically excited semiconductor superlattices [10][11][12]44] (see the review by Lyssenko & Leo [45]) and coupled optical waveguides [46,47], quantum gases in optical lattices realize practicable artificial solids with a higher degree of control and manipulation. They have, in fact, become a powerful experimental platform to explore matter waves' many-body interactions [1,2], matter waves' singular dynamics including electric quantum walks [48,49], super [6] and anomalous [50] Bloch oscillations as well as light-matter waves' interactions in stationary [43,[51][52][53][54][55][56][57][58] and moving [59][60][61][62] ordered atomic structures trapped in an optical lattice. Within this context, it is worth mentioning the recent work [63] on cold rubidium atoms trapped in an optical lattice and subject to external lasers that impart a circular motion to them, analogous to the motion of electrons in a strong magnetic field, with which self-similar fractal structures of the spectra (Hofstadter bands) are expected to be seen.…”