  We propose theoretically and demonstrate experimentally a generation of light
pulses whose polarization varies temporally to cover selected areas of the
Poincar\'e sphere with tunable swirling speed and total duration (1 ps and 10
ps respectively in our implementation). The effect relies on the Rabi
oscillations of two polarized fields in the strong coupling regime, excited by
two counter-polarized and delayed pulses. The interferences of the oscillating
fields result in the precession of the Stokes vector of the emitted light while
polariton lifetime imbalance results in its drift from a circle on the sphere
of controllable radius to a single point at long times. The positioning of the
initial and final states allows to engineer the type of polarization spanning,
including a full sweeping of the Poincar\'e sphere. The universality and
simplicity of the scheme should allow for the deployment of time varying
polarization fields at a technologically exploitable level.

Quantum Gases;Mesoscale and Nanoscale Physics;Optics