Dynamical localization in nonideal kicked rotors driven by two competing pulsatile modulations.

We study dynamical localization in an ultracold atom confined in an optical lattice that is simultaneously shaken by two competing pulsatile modulations with different amplitudes, periods, and waveforms. The effects of finite-width time pulses, modulation waveforms, and commensurable and incommensurable driving periods are investigated. We describe a particularly complex scenario and conclude that dynamical localization can survive, or even increase, when a periodic modulation is replaced by a quasiperiodic one of equal amplitude. Our analytical and numerical results indicate that there exists a strong correlation between the strengths of chaos (stochastic layer width) and dynamical localization (difference between the classical and quantum momentum dispersions) over the entire parameter space, which is maintained regardless of the periodic or quasiperiodic nature of the modulation. This persistent correlation provides a useful guide to optimally control the strength of dynamical localization by tuning the modulation parameters in real-world systems subjected to pulses of finite width.