The time-dependent polaron frame

The single-photon emitters in solid-state photonic devices have become crucial for quantum technology implementations. The exciton-phonon interaction degrades the quality of the photons even when the coherent scattering is dominant. Some models describing an emitter's trajectory in a phonon bath are the weak-coupling master equation and the standard and variational polaron master equations. The polaron theory based on a steady polaron transformation cannot capture the response of the phonon reservoir upon the exciton creation in its transformed Hamiltonian. Here, a time-dependent phonon displacement leads to the time evolution of the phonon-related energies and correlations. Variables as the phonon-induced energy shift and the phonon first-order correlation function converge to the standard polaron theory results. However, the expectation value of the phonon displacement operator differs. According to the time-dependent polaron master equation, the mitigation of the coupling between the single-photon emitter and the coherent driving field by the phonon reservoir evolves to be worse than predicted in the standard polaron theory.