Exciton polaritons in two-dimensional semiconductors inside microcavities are powerful platforms to explore hybrid light-matter quantum systems. Here, we study a macroscopic coherent population of the lowest energy state of polaron-polaritons, which are quasiparticles formed by the dressing of exciton polaritons by particle-hole excitations in a surrounding electron gas. Using a nonperturbative many-body theory to describe exciton-electron correlations combined with a nonequilibrium theory for the macroscopically populated state, we show that the electrons strongly affect the collective properties of the polaron-polaritons. This stems from the dependence of the polaron-polariton energy and the interaction between them on the electron density, which leads to strong nonlinearities. We identify stable and unstable regimes of the polaron-polaritons by calculating its excitation spectrum, and show that they result in prominent hysteresis effects when the electron density is varied. Our results should be readily observable using present experimental technology.

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• Bose-Fermi mixtures
• Exciton polariton
• Feynman diagrams
• Polaritons
• Polarons
• Semiconductor quantum optics
• Bose-Einstein condensates
• Nonequilibrium systems
• Semiconductor microcavities
• Transition metal dichalcogenides