Periodic driving is a versatile tool for probing and shaping the properties of a system. In many cases a description of the driven system is sought in terms of an effective time-independent reduction. I will present two examples of a nonperturbative periodic driving whose affect cannot be captured by such an approach, as the time-dependent solution displays properties inaccessible with a static system. I will focus on Paul traps, used to trap and cool atomic ions down to milliKelvin temperatures, where a periodic, parametric excitation is an essential part of the physics. The classical and quantum dynamics of driven Coulomb crystal, and the scattering of ultracold atoms from a driven ion, will be discussed in detail.

LPTMS Orsay