  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 experimental data from Ref.
[1]. We theoretically model the optical phase-imprinting technique employed to
experimentally excite finite-circulation states in Ref. [1] 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 $w_\mathrm{max}$ in the
superfluid ring. We also investigate the effect of a point-like obstacle with
variable potential height $V_0$ onto 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 favour 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 of the supercurrent decay rate for
increasing $w_0$, in agreement with experimental observations.
  [1]: G. Del Pace, et al., Phys. Rev. X 12, 041037 (2022)
