“…The polariton interactions, mediated by their excitonic part, make semiconductor microcavities a suitable platform for investigating a wide range of physical phenomena where coherence is a major issue, including Bose-Einstein condensation [2,3] or collective quantum fluid effects [4][5][6]. Experimentally, the coherent dynamics of polaritons have been investigated using four-wave mixing [5][6][7][8][9] and pumpprobe techniques [10][11][12][13], where the excitonic nonlinearity is evidenced through the changes in the optical response of the system. Theoretically, the coherent dynamics of polaritons are usually modeled using a nonlinear Schrödinger equation, which is formally equivalent to a Gross-Pitaevskii equations (GPE), often used for describing the coherent ground state of Bose condensed dilute atoms.…”