We analyze the stability and decay of supercurrents of strongly interacting bosons on optical lattices. At the mean-field level, the system undergoes an irreversible dynamic phase transition, whereby the current decays beyond a critical phase gradient that depends on the interaction strength. At commensurate filling the transition line smoothly interpolates between the classical modulational instability of weakly interacting bosons and the equilibrium Mott transition at zero current. Below the mean-field instability, the current can decay due to quantum and thermal phase slips. We derive asymptotic expressions of the decay rate near the critical current. In a three-dimensional optical lattice this leads to very weak broadening of the transition. In one and two dimensions the broadening leads to significant current decay well below the mean-field critical current. We show that the temperature scale below which quantum phase slips dominate the decay of supercurrents is easily within experimental reach.
We study the metastability and decay of multiply charged superflow in a ring-shaped atomic Bose-Einstein condensate. Supercurrent corresponding to a giant vortex with topological charge up to
q=10 is phase imprinted optically and detected both interferometrically and kinematically. We observe
q=3 superflow persisting for up to a minute and clearly resolve a cascade of quantized steps in its decay. These stochastic decay events, associated with vortex-induced $2\ensuremath{\pi}$ phase slips, correspond to collective jumps of atoms between discrete
q values. We demonstrate the ability to detect quantized rotational states with $>
99%$ fidelity, which allows a detailed quantitative study of time-resolved phase-slip dynamics. We find that the supercurrent decays rapidly if the superflow speed exceeds a critical velocity in good agreement with numerical simulations, and we also observe rare stochastic phase slips for superflow speeds below the critical velocity.