  Quantum vortices are the analogue of classical vortices in optics,
Bose-Einstein condensates, superfluids and superconductors, where they provide
the elementary mode of rotation and orbital angular momentum. While they
mediate important pair interactions and phase transitions in nonlinear fluids,
their linear dynamics is useful for the shaping of complex light, as well as
for topological entities in multi-component systems, such as full Bloch beams.
Here, setting a quantum vortex into directional motion in an open-dissipative
fluid of microcavity polaritons, we observe the self-splitting of the packet,
leading to the trembling movement of its center of mass, whereas the vortex
core undergoes ultrafast spiraling along diverging and converging circles, in a
sub-picosecond precessing fashion. This singular dynamics is accompanied by
vortex-antivortex pairs creation and annihilation, and a periodically changing
topological charge. The spiraling and branching mechanics represent a direct
manifestation of the underlying Bloch pseudospin space, whose mapping is shown
to be rotating and splitting itself. Its reshaping is due to three simultaneous
drives along the distinct directions of momentum and complex frequency, by
means of the differential group velocities, Rabi frequency and dissipation
rates, which are natural assets in coupled fields such as polaritons. This
state, displaying linear momentum dressed with oscillating angular momentum,
confirms the richness of multi-component and open quantum fluids and their
innate potentiality to implement sophisticated and dynamical topological
textures of light.
