Nonlinear Eigenmodes of a Polariton Harmonic Oscillator

Abstract

We investigate theoretically the quantum oscillator-like states recently observed experimentally in polariton condensates (Nat. Phys. 8, 190 (2012)). We consider a complex Gross-Pitaevskii type model which includes the effects of self-interactions, and creation and decay of exciton-polaritons. We develop a perturbation theory for approximate solutions to this non-equilibrium condensate model and compare the results with numerically calculated solutions for both repulsive and attractive polariton-polariton interactions. While the nonlinearity has a weak effect on the mode selection their density profiles are modified at moderate gain strengths and becomes more dominant when a very large gain of polaritons implies an extended cloud with high condensate densities. Finally, we identify the relation of the observed patterns to the input pump configuration, and suggest this may serve as a generalized NOR gate in the tradition of optical computing.