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In this work we perform a numerical study of a rotating, harmonicallytrapped, Bose-Einstein condensate of microcavity polaritons. An efficientnumerical method (toolbox) to solve the complex Gross-Pitaevskii equation isdeveloped. Using this method, we investigate how the behavior of the number ofvortices formed inside the condensate changes as the various system parametersare varied. In contrast to the atomic condensates, we show, there exists an(experimentally realizable) range of parameter values in which all the vorticescan be made to vanish even when there is a high rotation. We further explorehow this region can be tuned through other free parameters and also discuss howthis study can help to realize the synthetic magnetic field for polaritons andhence paving the way for the realization of the quantum Hall physics and manyother exotic phenomena.

Vortex Dynamics of Rotating Bose-Einstein Condensate of Microcavity Polaritons