Fluorescence in quantum dynamics: accurate spectra require post-mean-field approaches

Real time modelling of fluorescence with vibronic resolution entails the representation of the light-matter interaction coupled to a quantum-mechanical description of the phonons, and is therefore a challenging problem. In this work, taking advantage of the difference in time-scales characterizing internal conversion and radiative relaxation -which allows us to decouple these two phenomena by sequentially modelling one after the other- we simulate the electron dynamics of fluorescence through a master equation derived from the Redfield formalism. Moreover, we explore the use of a recent semiclassical dissipative equation of motion [ Phys. Rev. Lett. 126, 087401 (2021)], termed CEED, to describe the radiative stage. By comparing the results with those from the full quantum-electrodynamics treatment, we find that the semiclassical model does not reproduce the right amplitudes in the emission spectra when the radiative process involves the deexcitation to a manifold of closely lying states. We argue that this flaw is inherent to any mean-field approach, as it is the case of CEED. This effect is critical for the study of light-matter interaction and this work is, to our knowledge, the first one to report this problem. Besides, CEED reproduces the correct frequencies in agreement with quantum electrodynamics. This is a major asset of the semiclassical model, since the emission peak positions will be rightly predicted without any prior assumption about the nature of the molecular Hamiltonian. This is not so for the quantum electrodynamics approach, where access to the spectral information relies on the knowledge of the Hamiltonian eigenvalues.