Radiative thermalization in semiclassical simulations of light-matter interaction

Abstract

Prediction of the equilibrium populations in quantum dynamics simulations of molecules exposed to black-body radiation has proved challenging for semiclassical treatments, with the usual Ehrenfest and Maxwell-Bloch methods exhibiting serious failures. In this context, we explore the behavior of a recently introduced semiclassical model of light-matter interaction derived from a dissipative Lagrangian [C. M. Bustamante, E. D. Gadea, A. Horsfield, T. N. Todorov, M. C. González Lebrero, and D. A. Scherlis, Phys. Rev. Lett. 126, 087401 (2021)0031-900710.1103/PhysRevLett.126.087401]. It is shown that this model reproduces the Boltzmann populations for two-level systems, predicting the black-body spectra in approximate agreement with Planck's distribution. In multilevel systems, small deviations from the expected occupations are seen beyond the first excited level. By averaging over fast oscillations, a rate equation is derived from the dissipative equation of motion that makes it possible to rationalize these deviations. Importantly, it enables us to conclude that this model will produce the correct equilibrium populations provided the occupations of the lowest levels remain close to unity, a condition satisfied at low temperature or small excitations.