  The quantum diffusion of a vortex in a two-component quantum fluid of light
is investigated. In these systems, the Kerr nonlinearity promotes interactions
between the photons, displaying features that are analogue of a Bose-Einstein
condensates. Quantum fluids of light have the advantage of simulating
matter-wave phenomena at room temperatures. While the analogy is true at the
mean field level, the full quantum dynamics of an impurity in quantum fluids of
light of, and therefore the ability of featuring genuine quantum noise, has
never been considered. We numerically solve the problem by simulating a
vortex-like impurity in the presence of noise with the Bogoliubov spectral
density, and show that the vortex undergoes superdiffusion. We support our
results with a theory that has been previously developed for the brownian
motion of point-like particles.
