  Exciton-polariton condensates display a variety of intriguing pattern-forming
behaviors, particularly when confined in potential traps. It has previously
been predicted that triangular lattices of vortices of the same sign will form
spontaneously as the result of surface instabilities in a harmonic trap.
However, natural disorder, deviation of the external potential from circular
symmetry, or higher-order terms modifying the dynamical equations may all have
detrimental effects and destabilize the circular trajectories of vortices. Here
we address these issues, by characterizing the robustness of the vortex lattice
against disorder and deformations of the trapping potential. Since most
experiments use time integrated measurements it would be hard to observe
directly the rotating vortex lattices or distinguish them from vortex-free
states. We suggest how these difficulties can be overcome and present an
experimentally viable interference-imaging scheme that would allow the
detection of rotating vortex lattices.
