Quantum fluctuations in a strongly interacting Bardeen-Cooper-Schrieffer polariton condensate at thermal equilibrium

Microcavity electron-hole-photon systems in two dimensions have long been anticipated to exhibit a crossover from Bose-Einstein condensate (BEC) to Bardeen-Cooper-Schrieffer (BCS) superfluid when the carrier density is tuned to reach the Mott transition density. Yet, a theoretical understanding of such a BEC-BCS crossover largely relies on the mean-field framework and the nature of the carriers at the crossover remains unclear to some extent. Here, motivated by the recent demonstration of a BCS polariton laser [arXiv:1902.00142] and based on a simplified short-range description of the electron-hole attraction, we examine the role of quantum fluctuations in an exciton-polariton condensate at thermal equilibrium and determine the number of different types of carriers at the crossover beyond mean field. Near Mott density and with very strong light-matter coupling, we find an unexpectedly large phase window for a strongly correlated BCS polariton condensate, where both fermionic Bogoliubov quasiparticles and bosonic excitons are significantly populated and strongly couple to photons. We predict its absorption spectrum and show that the upper polariton energy gets notably renormalized, giving rise to a high-energy side-peak at large carrier density, as observed in recent experiments.