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We study nonlinear dynamics of exciton-polaritons in an incoherently pumped semiconductor microcavity with embedded weak-contrast lattice and coupled to an exciton reservoir. We elucidate fundamental features of non-equilibrium exciton-polariton condensate trapped in one-dimensional periodical potential close to zero momentum (so-called Zero-state) and to the state at the boundary of Brillouin zone ($pi$-state). Within the framework of the mean-field theory, we identify different regimes of both relaxation and oscillatory dynamics of coherent exciton-polaritons governed by superpositions of Bloch eigenstates within the periodic lattice. In particular, we theoretically demonstrate stable macroscopical oscillations, akin to nonlinear Josephson oscillations, between different spectral components of a polariton condensate in the momenta-space. We elucidate a strong influence of the dissipative effects and the feedback induced by the inhomogeneity of incoherent reservoir on the dynamics of the coherent polaritons.
We demonstrate, both experimentally and theoretically, a new phenomenon: the presence of dissipative coupling in the system of driven bosons. This is evidenced for a particular case of externally excited spots of exciton-polariton condensates in semi
We study the 2d phase transition of a driven-dissipative system of exciton-polaritons under non-resonant pumping. Stochastic calculations are used to investigate the Berezinskii-Kosterlitz-Thouless-like phase diagram for experimentally realistic para
We examine the photoluminescence of highly-excited exciton-polariton condensates in semiconductor microcavities. Under strong pumping, exciton-polariton condensates have been observed to undergo a lasing transition where strong coupling between the e
The generalized Gross-Pitaevskii equation (gGPE) is an effective phenomenological description for the dynamics of incoherently pumped exciton-polariton condensates. However, a brute force numerical simulation of the gGPE provides little physical insi
Microcavity exciton-polaritons are quantum quasi-particles arising from the strong light-matter coupling. They have exhibited rich quantum dynamics rooted from bosonic nature and inherent non-equilibrium condition. Dynamical condensation in microcavi