We construct a theory for Bose-Einstein condensation of light in nanofabricated semiconductor microcavities. We model the semiconductor by one conduction and one valence band which consist of electrons and holes that interact via a Coulomb interaction. Moreover, we incorporate screening effects by using a contact interaction with the scattering length for a Yukawa potential and describe in this manner the crossover from exciton gas to electron-hole plasma as we increase the excitation level of the semiconductor. We then show that the dynamics of the light in the microcavities is damped due to the coupling to the semiconductor. Furthermore, we demonstrate that on the electron-hole plasma side of the crossover, which is relevant for the Bose-Einstein condensation of light, this damping can be described by a single dimensionless damping parameter that depends on the external pumping. Hereafter, we propose to probe the superfluidity of light in these nanofabricated semiconductor microcavities by making use of the differences in the response in the normal or superfluid phase to a sudden rotation of the trap. In particular, we determine frequencies and damping of the scissors modes that are excited in this manner. Moreover, we show that a distinct signature of the dynamical Casimir effect can be observed in the density-density correlations of the excited light fluid.
We study the Bose polaron problem in a nonequilibrium setting, by considering an impurity embedded in a quantum fluid of light realized by exciton-polaritons in a microcavity, subject to a coherent drive and dissipation on account of pump and cavity losses. We obtain the polaron effective mass, the drag force acting on the impurity, and determine polaron trajectories at a semiclassical level. We find different dynamical regimes, originating from the unique features of the excitation spectrum of driven-dissipative polariton fluids, in particular a non-trivial regime of acceleration against the flow. Our work promotes the study of impurity dynamics as an alternative testbed for probing superfluidity in quantum fluids of light.