Correlated photon dynamics in dissipative Rydberg media
Describing the driven-dissipative dynamics of many-body systems is an exciting frontier of theoretical physics. In this work, we studied the emergent non-equilibrium behavior of a system of interacting photons. The interactions arise from dressing photons with highly excited Rydberg states in cold atomic gases. In the limit of strong dissipative interactions, whereby two photons destroy each other when they overlap in space, we found that a uniform, large amplitude coherent state input into the medium will be transformed into a liquid of single photons on the output with crystalline correlations. Although the crystalline correlations do not display true long range order, if this crystalline order could be stabilized through other means, this system would provide a novel realization of a time-crystal.