Non-perturbative treatment of quantum dots coupled to light and phonons

We present an exact solution for the dynamics of a quantum dot (QD) coupled to phonons and excited by ultra-short light pulses. The solution is non-perturbative with respect to both carrier-phonon and carrier-light coupling, and accounts for an arbitrary number of pulses. Explicit expressions for the one and two pulse solutions are used to obtain the non-linear four-wave-mixing optical response by a single QD as well as by disordered QD arrays. Phonon emission by the excited QD is shown to be qualitatively different from that in the phonon assisted carrier relaxation.