In  the dynamical localization is predicted for periodically current-driven Josephson junctions: the quantum-mechanical decrease, as opposite to the classical increase, of the intensity of voltage fluctuations with increasing driving amplitude. Classically, this intensity is predicted to rise linearly with the current amplitude. The effect of dynamical localization of chaos gives the decrease of this intensity in inverse proportionality to the current amplitude, above a certain current threshold.
Later, Graham et al. noted that the quantum model introduced and studied in  describes also the dynamics of atoms in a resonator with modulated boundary. Here the momentum of atom is analogous to the voltage in the case of Josephson junction. This model was realised in the laboratory experiments with laser cooled atoms by group of Raizen (Austin, TX) in 1994 - 1995. This group worked in the dimensionless parameter regime proposed in  and clearly observed quantum localization of chaos. Later, the Raizen group introduced sharp modulation of the boundary and in this way directly realised the kicked rotator model with dynamical localization of chaos.