Dynamical Control of Phases in an Atom-Cavity System
One intriguing phenomenon in nature is the rich interplay between coexisting phases or competing orders in various complex systems. We recently studied the effects of external driving on coexisting phases by considering a Bose-Einstein condensate (BEC) inside a high-finesse optical cavity. First, I will introduce the physical system consisting of the BEC and the leaky optical cavity. This system hosts a competition between a homogeneous BEC phase and a self-organized density wave phase. Motivated by the challenges of light-induced superconductivity, we demonstrate dynamical control of this phase transition via periodic driving of the pump laser. I will also present experimental results, which confirm our prediction of light-induced condensation in the atom-cavity system. Furthermore, we show that additional, nonequilibrium density wave orders, which do not exist in equilibrium, can be stabilized dynamically. I will present how shaking the BEC inside the cavity can lead to the emergence of a novel nonequilibrium phase - a discrete time crystal, which breaks both space- and time-translation symmetry.