  The Jaynes-Cummings model, describing the interaction between a single
two-level system and a photonic mode, has been used to describe a large variety
of systems, ranging from cavity quantum electrodynamics, trapped ions, to
superconducting qubits coupled to resonators. Recently there has been renewed
interest in studying the quantum strong-coupling (QSC) regime, where states
with photon number greater than one are excited. This regime has been recently
achieved in semiconductor nanostructures, where a quantum dot is trapped in a
planar microcavity. Here we study the quantum strong-coupling regime by
calculating its photoluminescence (PL) properties under a pulsed excitation. We
discuss the changes in the PL as the QSC regime is reached, which transitions
between a peak around the cavity resonance to a doublet. We particularly
examine the variations of the PL in the time domain, under regimes of short and
long pulse times relative to the microcavity decay time.
