  We employ a quantum master equations approach based on a vectorial
Maxwell-pseudospin model to compute the quantum evolution of the spin
populations and coherences in the fundamental singlet trion transition of a
negatively charged quantum dot embedded in a micropillar cavity. Excitation of
the system is achieved through an ultrashort, either circularly or linearly
polarised resonant pulse. By implementing a realistic micropillar cavity
geometry, we numerically demonstrate a giant optical phase shift ($\sim \pm
\pi/2$) of a resonant circularly polarised pulse in the weak-coupling regime.
The phase shift that we predict considerably exceeds the experimentally
observed Kerr rotation angle $(\sim{6 ^{\circ}})$ under a continuous-wave,
linearly polarised excitation. By contrast, we show that a linearly polarised
pulse is rotated to a much lesser extent of a few degrees. Depending on the
initial boundary conditions, this is due to either retardation or advancement
in the amplitude build-up in time of the orthogonal electric field component.
Unlike previous published work, the dominant spin relaxation and decoherence
processes are fully accounted for in the system dynamics. Our dynamical model
can be used for optimisation of the optical polarisation rotation angle for
realisation of spin-photon entanglement and ultrafast polarisation switching on
a chip.
