Polaritons in an electron gas -- quasiparticles and Landau effective interactions

Two-dimensional semiconductors inside optical microcavities have emerged as a versatile platform to explore new hybrid light-matter quantum states. The strong light-matter coupling leads to the formation of exciton-polaritons, which in turn interact with the surrounding electron gas to form quasiparticles called polaron-polaritons. Here, we develop a general microscopic framework to calculate the properties of these quasiparticles such as their energy and the interactions between them. From this, we give microscopic expressions for the parameters entering a Landau theory for the polaron-polaritons, which offers a simple yet powerful way to describe such interacting light-matter many-body systems. As an example of the application of our framework, we then use the ladder approximation to explore the properties of the polaron-polaritons. We furthermore show that they can be measured in a non-demolition way via the light transmission/reflection spectrum of the system. Finally, we demonstrate that the Landau effective interaction mediated by electron-hole excitation is attractive leading to red shifts of the polaron-polaritons. Our work provides a systematic framework to study exciton-polaritons in electronically doped two-dimensional materials such as novel van der Waals heterostructures.