Realisation of full-Bloch beams with ultrafast Rabi-rotating vortices.

Strongly-coupled quantum fluids, such as multi-component atomic condensates, optical fields and polaritons, are remarkable systems that allow to test the most fundamental symmetries and conservation laws of Physics. When the coupling between the components is coherent, not only the particles number, but also their phase texture that maps the linear and angular momentum, can be exchanged. Here, using optical pulses of different topologies and their coherent control, we excite the multi-component fluid of exciton-polaritons in such a way that all quantum states on the Bloch sphere are simultaneously present and undergo a structured Rabi-oscillatory dynamics. As a result, the complex light emitted from the cavity is characterized by inner phase singularity tubes spiraling around their axis of propagation, i.e., we observe a new kind of swirling vortices endowed with oscillating linear and orbital momentum, which exhibit ultrafast motion with striking accelerations beyond superluminal speed. This vortex motion is tracked by means of the stereographic projection, thanks to the created homeomorphism between the Bloch sphere and the real physical plane, and expressed in terms of the M\"obius transformation.