Structure formation, superfluid velocity patterns, and induced vortex-antivortex oscillations and rotations in microcavity polaritons

We use the nonequilibrium Gross-Pitaevskii equation in the form recently derived [H. Haug et al., Phys. Rev. B 89, 155302 (2014)] to study spontaneous pattern formation and the connected superfluid current patterns. Using a nonresonant excitation beam with ring structure we get depending on the details of the structure and of the pump power, different spatial patterns of the condensate density. The corresponding phase profiles allow to identify, e.g., vortex-antivortex pairs, but beyond that, yield an image of the superfluid flow patterns linked with the structured condensate density. The fast superfluid flow driven by the spatially changing phase with velocities of the order of several m mu/ps is found to be often supersonic. In order to test dynamically the stability of the spontaneously formed flow patterns under external perturbations, we apply an additional resonant Laguerre-Gauss beam with angular momentum. This beam causes complex response of the phase patterns. This response is shown to be basically an oscillation or rotation of the vortex-antivortex pair depending on the strength of the extra beam. The rotation is induced via a ring of vortices induced by the Laguerre-Gaus beam. The main result of these studies is the extraordinary stability of the vortex-antivortex pair even under strongly perturbing external fields.