Positronium density measurements using polaritonic effects

Recent experimental advances in positronium (Ps) physics have made it possible to produce dense Ps ensembles in which Ps-Ps interactions may occur, leading to the production of Ps2 molecules and paving the way to the realization of a Ps Bose-Einstein condensate (BEC). In order to achieve this latter goal it would be advantageous to develop new methods to measure Ps densities in real time. Here we describe a possible approach to do this using polaritonic methods: Using realistic experimental parameters, we demonstrate that a dense Ps gas can be strongly coupled to the photonic field of a distributed Bragg reflector microcavity. In this strongly coupled regime, the optical spectrum of the system is composed of two hybrid positronium-polariton resonances separated by the vacuum Rabi splitting, which is proportional to the square root of the Ps density. Given that polaritons can be created on a subcycle timescale, a spectroscopic measurement of the vacuum Rabi splitting could be used as an ultrafast Ps density measurement in regimes relevant to Ps BEC formation. Moreover, we show how positronium polaritons could potentially enter the ultrastrong light-matter coupling regime, introducing a platform to explore its nonperturbative phenomenology.