Radiative pumping vs vibrational relaxation of molecular polaritons: a bosonic mapping approach

We present a formalism to study molecular polaritons in the collective regime, based on the bosonization of molecular vibronic states. This formalism accommodates an arbitrary number of molecules N, excitations and internal vibronic structures, making it ideal for investigating molecular polariton processes beyond the N→∞ limit (i.e., accounting for finite N effects), both numerically and analytically. Here, we employ this formalism to rigorously derive radiative pumping and vibrational relaxation rates, and establish the fundamental differences between these mechanisms. We show that radiative pumping is the emission from incoherent excitons and divide its rate into transmitted and re-absorbed components. On the other hand, the vibrational relaxation rate in the weak linear vibronic coupling regime is composed of two components: a O(1/N) contribution already accounted for by radiative pumping, and a O(1/N²) contribution from a second-order process in the single-molecule light-matter coupling that we identify as a polariton-assisted Raman scattering. We demonstrate that vibrational relaxation via this scattering is enhanced when the energy difference between the emission and the lower polariton transition corresponds to the vibrational excitation created in the Raman process.