Dynamical freezing in Periodically Driven Quantum Systems

In recent years, periodic driving has emerged as a powerful tool for the coherent control of quantum many-body systems. However, these systems suffer from an inherent drawback – they absorb energy from the drive and eventually thermalize to a featureless infinite temperature state. In this talk, I will propose a route to evade this `heat death’ by realizing dynamical freezing. In the first part of the talk, I will discuss a many-body interference mechanism that harnesses dynamical freezing to create an eternal discrete time crystal in a system with all-to-all interactions. In the second part of the talk, I will describe a two-tone driving protocol to realize exact Floquet flat bands in a large class of many-body systems. The Floquet Flat bands lead to dynamical freezing and a strong violation of the eigenstate thermalization hypothesis. In the vicinity of these points, heating is suppressed up to very long timescales in such driven systems, leading to a prethermal regime. The corresponding micromotion exhibits coherent reversal of excitations reminiscent of echoes. Our analysis constitutes a yet unexplored mechanism for heating suppression in driven closed quantum systems.