The rise and fall of patterns in driven-dissipative Rydberg polaritons

Spatial structures commonly emerge in interacting nonlinear systems. In this study, we focus on the out-of-equilibrium dynamics of the recently-established platform of Rydberg exciton-polaritons, fueled by their characteristic long-range non-local interactions, in the presence of an external drive and dissipation. Our work elucidates how modulational instability sets off spontaneous density pattern formations in a Rydberg polariton system with characteristic scales in the micron range. Under conditions of an unstable flattop state, we track the evolution of the polariton ensemble, showing the emergence of meta-stable patterns and their collapse in the long-time limit. We trace this phenomenon back to the destructive interference between the polariton state and the pump in a driven ensemble. Finally, we map out conditions that allow stable patterns to form under incoherent pumping. These findings provide new opportunities for exploring the emerging field of long-range interacting gases through Rydberg exciton-polaritons.