Steering interchange of polariton branches via coherent and incoherent dynamics

Controlling light-matter-based quantum systems in the strong coupling regime allows for exploring quantum simulation of many-body physics in current architectures. For instance, the atom-field interaction in a cavity QED network provides control and scalability for quantum information processing. Here, we propose the control of single- and two-body Jaynes-Cummings systems in a nonequilibrium scenario, which allows us to establish conditions for the coherent and incoherent interchange of polariton branches. Our findings provide a systematic approach to manipulate the interchange of polaritons, which we apply to reveal insights into the transition between Mott-insulator- and superfluid-like states. Furthermore, we study the asymmetry in the absorption spectrum by triggering the cavity and atomic losses as a function of the atom-cavity detuning and the photon's hopping.