  We study the vortex dynamics of a quantum degenerate Bose gas through the
intensity fluctuations of the interference from particles extracted at two
different positions. It is shown numerically with classical field simulations
that an interacting Bose gas with proliferating vortices exhibits long
correlation times for these intensity fluctuations. This behavior is contrasted
with the case of a noninteracting gas, that we describe analytically, and with
the case of a well condensed Bose gas without vortices. We discuss the
observability of our predictions in quantum fluids of exciton-polaritons.
