Cold atom optics has provided faithful experimental realizations of paradigmatic albeit abstract models of quantum chaology. The significance of such experiments has gone well beyond the level of quantum optical engineering, because experimentally introduced variants to the ideal models have exposed unexpected new phenomena. Subsequent theoretical analysis has brought to light unsuspected connections to famous aspects of nonlinear dynamics, such as the mode (frequency) locking phenomenon, the Arnol'd tongues, and number-theoretic aspects thereof..
These aspects, to be quickly reviewed, are a familiar occurence with dissipative driven systems. In contrast, here they are observed in purely quantal, fully coherent context. Reflecting this fundamental difference, their analysis shows that they belong in a different universality class from the instances of mode-locking which were most widely studied so far.