Topological constraints on the dynamics of vortex formation in a bi-dimensional quantum fluid

We present experimental and theoretical results on formation of quantum vortices in a laser beam propagating in a nonlinear medium. Topological constrains richer that the mere conservation of vorticity impose an elaborate dynamical behavior to the formation and annihilation of vortex/anti-vortex pairs. We identify two such mechanisms, both described by the same fold-Hopf bifurcation. One of them is particularly efficient although it is not observed in the context of liquid helium films or stationary linear systems because it relies on the finite compressibility and on the non-stationnarity of the fluid of light we consider.