We study the long-time dynamics and the stationary nonequilibrium state of an optically driven quantum dot coupled to acoustic phonons using numerically exact real-time path integrals and a fourth-order correlation expansion. By exploring wide ranges of temperatures, carrier-phonon and carrier-light coupling strengths, we characterize the stationary nonequilibrium state and compare the exact solution to known, approximatively derived results. It is found that analytical calculations tend to overestimate the influence of the carrier-phonon coupling, particularly at low temperatures and in the weak-coupling regime. The possibility of controlling the dot occupation in the stationary nonequilibrium by varying the laser detuning is discussed. A comparison between the numerical methods identifies the range of validity of the correlation expansion, which in the long-time limit is found to be surprisingly wide.

• Received 5 July 2011

DOI:https://doi.org/10.1103/PhysRevB.84.195311