Bogoliubov dispersion relation and the possibility of superfluidity for weakly-interacting photons in a 2D photon fluid

The Bogoliubov dispersion relation for the elementary excitations of the weakly-interacting Bose gas is shown to hold for the case of the weakly-interacting photon gas (the ``photon fluid'') in a nonlinear Fabry-Perot cavity. This relation, which is also derived by means of a linearized fluctuation analysis in classical nonlinear optics, implies the possibility of a new superfluid state of light. The theory underlying an experiment in progress to measure this dispersion relation is described, and another experiment to test the prediction of the superfluidity of this state of light is proposed.