Positronium density measurements using polaritonic effects

Recent experimental advances in Positronium (Ps) physics have made it possible to produce dense Ps ensembles which Ps-Ps interactions may occur, leading the production of Ps$_2$ molecules and paving way realization a Bose-Einstein Condensate (BEC). In order achieve this latter goal would be advantageous develop new methods measure densities real-time. Here we describe approach do using polaritonic methods: realistic parameters demonstrate that gas can strongly coupled photonic field distributed Bragg reflector microcavity. regime, optical spectrum system is composed two hybrid positronium-polariton resonances separated by vacuum Rabi splitting, proportional square root density. Given polaritons created on sub-cycle timescale, spectroscopic measurement splitting could used as an ultra-fast density regimes relevant BEC formation. Moreover, show how positronium-polaritons potentially enter ultrastrong light-matter coupling introducing radically novel platform explore its non-perturbative phenomenology.