Abstract
We propose a way to directly excite compact localized condensates in a nearly flat band of the exciton-polariton Lieb lattice by short Laguerre-Gaussian pulses and investigate the dynamics of these condensates in the presence of repulsive polariton-polariton interaction and distributed losses in the lattice. The evolution of a low-density compact polariton condensate shows fast Rabi oscillations between its excitonic and photonic components, with slow beatings of the Rabi oscillation amplitude. Both oscillations and beatings are suppressed at higher condensate densities due to polariton-polariton repulsion and distributed losses in the lattice. A background incoherent pumping can be used to increase the lifetime and stability of compact localized states
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