Kibble-Zurek scaling in periodically driven quantum systems

We study the slow crossing of non-equilibrium quantum phase transitions in periodi- cally driven systems. We explicitly consider a spin chain with a uniform time-dependent magnetic field and focus on the Floquet state that is adiabatically connected to the ground state of the static model. We find that this Floquet ground state undergoes a series of quantum phase transi- tions characterized by a non-trivial topology. To dynamically probe these transitions, we propose to start with a large driving frequency and slowly decrease it as a function of time. Combining analytical and numerical methods, we uncover a Kibble-Zurek scaling that persists in the presence of moderate interactions. This scaling can be used to experimentally demonstrate non-equilibrium transitions that cannot be otherwise observed.