# PRL on Tensor Network Simulation of Non-Markovian Dynamics in Organic Polaritons

We just published an article in Physical Review Letters on “Tensor Network Simulation of Non-Markovian Dynamics in Organic Polaritons”. This work is closely related to our recent paper in Phys. Rev. B, and was actually submitted first, but took a bit longer before it was accepted for publication. Instead of the static properties of the lower polaron-polariton (i.e., the lowest-energy excited state), we here treat the temporal dynamics after sudden excitation of the system to the “bare” upper polariton without vibrational dressing.

In this work, optical, vibrational, and radiative processes are treated on an equal footing employing the time-dependent variational matrix product states algorithm in which the many-body wave function of the system is described by a tree tensor network. We demonstrate signatures of non-Markovian vibronic dynamics, which means that the vibrational modes of the molecules cannot be treated like a random “memory-less” bath that just leads to decoherence in the dynamics of the excitons and photons. Instead, we find coherent oscillations in the vibrational degrees of freedom that couple between different polaritonic (hybrid electronic-photonic) states and significantly affect the dynamics.

In addition, due to the ability of our numerical algorithm to treat a large number of quantum degrees of freedom explicitly, we could include free-space photons explicitly in our wave function and calculate the (ultrafast) emission spectrum from the nanocavity for arbitrary values of the light-matter interaction ranging from the weak to the strong coupling regimes. We analyzed both the single- and many-molecule cases, showing the crucial role played by the collective motion of the molecular nuclei and dark states in determining the polariton dynamics and the subsequent photon emission.