Efficient many-body non-Markovian dynamics of organic polaritons

We show how to simulate a model of many molecules with both strong coupling to many vibrational modes and collective coupling to a single photon mode. We do this by combining process tensor matrix product operator methods with a mean-field approximation which reduces the dimension of the problem. We analyze the steady-state of the model under incoherent pumping to determine the dependence of the polariton lasing threshold on cavity detuning, light-matter coupling strength, and environmental temperature. Moreover, by measuring two-time correlations, we study quadratic fluctuations about the mean-field to calculate the photoluminescence spectrum. Our method enables one to simulate many-body systems with strong coupling to multiple environments, and to extract both static and dynamical properties.