  Vortices are topological objects formed in coherent nonlinear systems. As
such they are studied in a wide number of physical systems and promise
applications in information storage, processing, and communication. In
semiconductor microcavities, vortices in polariton condensates can be
conveniently created, studied, and manipulated using solely optical means. For
non-resonant excitation with a ring-shaped pump a stable vortex can be formed,
leading to bistability with left- and righthanded vorticity. In the present
work we report on a much richer vortex multistability, with optically
addressable vortices with topological charges |m|=1, 2, and 3, all stable for
the same system and excitation parameters. This unusual multistable behavior is
rooted in the inherent nonlinear feedback between reservoir excitations and
condensate in the microcavity. For larger radius of the ring shaped pump we
also find a Bessel vortex with its characteristic spiralling phase in the high
density region and pronounced self-stabilization ability. Our theoretical
results open up exciting possibilities for optical manipulation of vortex
multiplets in a compact semiconductor system.
