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We introduce an intuitive and semi-analytical polaron master equationapproach to model pulse-driven population inversion and emitted single photonsfrom a quantum dot exciton. The master equation theory allows one to identifyimportant phonon-induced scattering rates analytically, and fully includes therole of the time-dependent pump field. As an application of the theory, wefirst study a quantum dot driven by a time-varying laser pulse on and offresonance, showing the population inversion caused by acoustic phonon emissionin direct agreement with recent experiment of Quilter {\em et al.}, Phys RevLett {\bf 114}, 137401 (2015). We then model quantum dots in weakly coupledcavities and show the difference in population response between exciton-drivenand cavity-driven systems. Finally, we assess the nonresonant phonon-assistedloading scheme with a quantum dot resonantly coupled to a cavity as adeterministic single photon source, and compare and contrast the importantfigures of merit with direct Rabi oscillation of the population using aresonant $\pi$ pulse, where the latter is shown to be much more efficient.

Polaron master equation theory of pulse driven phonon-assisted population inversion and single photon emission from quantum dot excitons