We investigate the role of vortices in the decay of persistent current states of annular atomic superfluids by solving numerically the Gross-Pitaevskii equation, and we directly compare our results with the Li-6 experiment at LENS data. We theoretically model the optical phase-imprinting technique employed to experimentally excite finite-circulation states in the Bose-Einstein condensation regime, accounting for imperfections of the optical gradient imprinting profile. By comparing simulations of this realistic protocol to an ideal imprinting, we show that the introduced density excitations arising from imperfect imprinting are mainly responsible for limiting the maximum reachable winding number w(max) in the superfluid ring. We also investigate the effect of a point-like obstacle with variable potential height V-0 on the decay of circulating supercurrents. For a given obstacle height, a critical circulation w(c) exists, such that for an initial circulation w(0) larger than w(c) the supercurrent decays through the emission of vortices, which cross the superflow and thus induce phase slippage. Higher values of the obstacle height V-0 further favor the entrance of vortices, thus leading to lower values of w(c). Furthermore, the stronger vortex-defect interaction at higher V-0 leads to vortices that propagate closer to the center of the ring condensate. The combination of both these effects leads to an increase in the supercurrent decay rate for increasing w(0), in agreement with experimental observations.
