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We study the nucleation and dynamics of vortices in rotating latticepotentials where weakly linked condensates are formed with each condensateexhibiting an almost axial symmetry. Due to such a symmetry, the on-site phasesacquire a linear dependence on the coordinates as a result of the rotation,which allows us to predict the position of vortices along the low density pathsthat separate the sites. We first show that, for a system of atoms loaded in afour-site square lattice potential, subject to a constant rotation frequency,the analytical expression that we obtain for the positions of vortices of thestationary arrays accurately reproduces the full three-dimensionalGross-Pitaevskii results. We then study the time-dependent vortex nucleationprocess when a linear ramp of the rotation frequency is applied to a latticewith sixteen sites. We develop a formula for the number of nucleated vorticeswhich turns to have a linear dependence on the rotation frequency with asmaller slope than that of the standard estimate which is valid in absence ofthe lattice. From time-dependent Gross-Pitaevskii simulations we further findthat the on-site populations remain almost constant during the time evolutioninstead of spreading outwards, as expected from the action of the centrifugalforce. Therefore, the time-dependent phase difference between neighboring sitesacquires a running behavior typical of a self-trapping regime. We finally showthat, in accordance with our predictions, this fast phase-difference evolutionprovokes a rapid vortex motion inside the lattice. Our analytical expressionsmay be useful for describing other vortex processes in systems with the sameon-site axial symmetry.

Vortex nucleation processes in rotating lattices of Bose-Einstein condensates ruled by the on-site phases