Engineering non-Hermitian optical potentials for Polariton Condensation

We present a theoretical study of incoherently pumped exciton-polariton condensates in general cavity geometries, based on an analysis of the linear non-Hermitian modes of the (optical) pump induced potential. An analytical description is obtained for how the threshold pump power for condensation into a specific mode depends quantitatively on the relative spatial profiles of that mode and the pump. Specifically, we show that for a general pump profile, modes which best organize to balance the amplification from the pump against the repulsive pump potential achieve the lowest threshold power~[1]. Reversing this idea, choosing the spatial profile of the pump provides control over which spatial mode condenses at lowest power. Our work hence provides a scheme to engineer non-Hermitian optical potentials for preferential polariton condensation into a specific mode, by an appropriate choice of pump profile. This approach has recently been used to achieve condensation in the flat band of a Lieb chain of micropillar cavities, where the flat band has energy above the ground state and hence cannot be studied in systems in thermal equilibrium~[2]. \\ \textbf{References:} \\ {[}1{]} L. Ge, \emph{et. al.}, arXiv: 1311.4847 (2013) \\ {[}2{]} F. Baboux \emph{et. al.}, arXiv: 1505.05652 (2015)