Dynamics of Quantum Phase Transition in an Array of Josephson Junctions

We study the dynamics of the Mott insulator-superfluid quantum phase transition in a periodic 1D array of Josephson junctions. We show that crossing the critical point at a finite rate with a quench time ${\tau }_Q$ induces finite quantum fluctuations of the current around the loop proportional to ${\tau }_Q^{-1/6\mathrm{}}$. This scaling could be experimentally verified with an array of weakly coupled Bose-Einstein condensates or superconducting grains.