Interplay between classical and quantum dissipation in light-matter dynamics

A quantum-electrodynamics approach is presented to describe the dynamics of electrons that exchange energy with both photon and phonon baths. Our ansatz is a dissipative quantum Liouville equation, cast in the Redfield form, with two driving terms associated with radiative and vibrational relaxation mechanisms, respectively. Remarkably, within the radiative contribution, there is a term that exactly replicates the expression derived from a semiclassical treatment where the power dissipated by the electronic density is treated as the emission from a classical dipole [Bustamante et al., Phys. Rev. Lett. 126, 087401 (2021)]. Analysis of the distinct contributions to the total radiation shows that the semiclassical emission depends on the coherences, with the remainder of the quantum-electrodynamics driving term determined by the excited populations, thus accounting for the relaxation of eigenstates or incoherent mixed states. This approach is used to investigate the response of the Su-Schrieffer-Heeger model for trans-polyacetylene to both pulsed and continuous laser irradiation. Upon excitation with a short pulse and in the absence of the vibrational mechanism, the conducting band population exhibits a stepwise relaxation, characterized by cycles of exponential decay followed by a transient subradiant state. The latter arises from the collective coupling between Bloch states featuring a quasi-continuum energy spectrum in reciprocal space. The separate examination of the semiclassical dynamics reveals that it is this contribution that is responsible for the collective behavior. If vibrational dissipation is active, following the laser pulse, the excited electrons rapidly populate the minimum of the conduction band, and the emission spectrum shifts to lower frequencies with respect to absorption. Meanwhile, continuous irradiation drives the system to a stationary state with a broad emission spectrum.