Quantum decay of the persistent current in a Josephson junction ring

Abstract

We study the persistent current in a ring consisting of N≫1 Josephson junctions threaded by the magnetic flux. When the dynamics of the ring is dominated by the capacitances of the superconducting islands the system is equivalent to the xy spin system in 1+1 dimensions at the effective temperature T*=2JU, with J being the Josephson energy of the junction and U being the charging energy of the superconducting island. The numerical problem is challenging due to the absence of thermodynamic limit and slow dynamics of the Kosterlitz-Thouless transition. It is investigated on lattices containing up to ×106 sites. At T*≪J the quantum phase slips are frozen. The low-T* dependence of the persistent current computed numerically agrees quantitatively with the analytical formula provided by the spin-wave approximation. The high-T* behavior depends strongly on the magnetic flux and on the number of superconducting islands N. We present a detailed numerical study of the unbinding of vortex-antivortex pairs responsible for the phase slips, the superconductor-insulator transition, and evolution of the persistent current in a finite-size system.

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