Massive phonons and gravitational dynamics in a photon-fluid model

We theoretically investigate the excitation dynamics in a photon fluid with both local and nonlocal interactions. We show that the interplay between locality and an infinite-range nonlocality gives rise to a gapped Bogoliubov spectrum of elementary excitations which, at lower momenta, correspond to massive particles (phonons) with a relativistic energy-momentum relation. In this regime and in the presence of an inhomogeneous flow the density fluctuations are governed by the massive Klein-Gordon equation on the acoustic metric and thus propagate as massive scalar fields on a curved spacetime. We finally demonstrate that in the nonrelativistic limit the phonon modes behave as self-gravitating quantum particles with an effective Schrodinger-Newton dynamics, although with a finite-range gravitational interaction and a nonzero cosmological constant. Our photon fluid represents a viable alternative to Bose-Einstein condensate models for "emergent gravity" scenarios and offers a promising setting for analog simulations of semiclassical gravity and quantum gravity phenomenology.