Time Crystals 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. In this talk, I will propose a route to realize a time crystal in a periodically driven quantum system. A time crystal is a fascinating non-equilibrium phase of matter that exhibits spontaneous time-translation-symmetry breaking. I will demonstrate that a many-body interference mechanism can be harnessed to create an eternal time crystal with global "all-to-all" interactions. If time permits, I will also discuss the stability of this time crystalline order, when the drive becomes aperiodic.