Polaron relaxation in a quantum dot due to anharmonic coupling within a mean-field approach

We study the electronic relaxation in a quantum dot within the polaron approach, by focusing on the {\it reversible} anharmonic decay of longitudinal optical (LO) phonons forming the polaron into longitudinal acoustic (LA) phonons. The coherent coupling between the LO and LA phonons is treated within a mean-field approach. We derive a temperature-dependent inter-level coupling parameter, related to the Gr\"uneisen parameter and the thermal expansion coefficient, that characterizes an effective decay channel for the electronic (or excitonic) states. Within this theory, we obtain a characteristic anharmonic decay time of 1ns, 2-3 orders of magnitude longer than previous predictions based on the Fermi's Golden Rule. We suggest that coherent relaxation due to carrier-carrier interaction is an efficient alternative to the (too slow) polaron decay.