Non-Markovian effects in long-range polariton-mediated energy transfer

Intramolecular energy transfer driven by near-field effects plays an important role in applications ranging from biophysics and chemistry to nano-optics and quantum communications. Advances in strong light-matter coupling in molecular systems have opened new possibilities to control energy transfer. In particular, long-distance energy transfer between molecules has been reported as the result of their mutual coupling to cavity photon modes and the formation of hybrid polariton states. In addition to strong coupling to light, molecular systems also show strong interactions between electronic and vibrational modes. The latter can act as a reservoir for energy to facilitate off-resonant transitions and, therefore, energy relaxation between polaritonic states at different energies. However, the non-Markovian nature of these modes makes it challenging to accurately simulate these effects. Here, we capture them via process tensor matrix product operator methods to describe exactly the vibrational environment of the molecules combined with a mean-field treatment of the light-matter interaction. In particular, we study the emission dynamics of a system consisting of two spatially separated layers of different species of molecules coupled to a common photon mode and show that the strength of coupling to the vibrational bath plays a crucial role in governing the dynamics of the energy of the emitted light; at strong vibrational coupling, this dynamics shows strongly non-Markovian effects, eventually leading to polaron formation. Our results shed light on polaritonic long-range energy transfer and provide further understanding of the role of vibrational modes of relevance to the growing field of molecular polaritonics.