Polariton condensation in 2D Lieb lattice with distributed dissipation

While one flat band appears in the 2D Lieb lattice in the tight binding model, it is hard to yield any flatness in realistic continuous models for polaritons propagating in the presence of lateral potential mimicking the Lieb lattice structure. Nevertheless, in this work, we show the exciton-polariton condensation can happen in the states possessing the symmetry of compact localized states that characterize the flat band. We consider the two-dimensional system of exciton-polaritons in semiconductor microcavity patterned with the Lieb potential. Due to the dissipative nature of this system, the single polariton motion is described by the complex periodic 2D potential, where the dissipation rate from the quantum wells differs from dissipation rate from the potential barriers. This reflects the typical experimental situation of different leakage from the wells and the barriers. Solving the Gross-Pitaevskii equation coupled to an external reservoir, we show that, under certain conditions, it becomes easier for the second (nearly flat) band to reach the condensation threshold. Thus, the condensate is formed in a non-trivial many-body state. The properties of this state are characterized by calculation of the first-order spatial correlation function g⁽¹⁾ for different lattice sites.