Quantum phase slips in Josephson junction rings

We study quantum phase-slip (QPS) processes in a superconducting ring containing N Josephson junctions and threaded by an external static magnetic flux ?. In such a system, a QPS consists of a quantum tunneling event connecting two distinct classical states of the phases with different persistent currents. When the Josephson coupling energy E of the junctions is larger than the charging energy E=e2/2C, where C is the junction capacitance, the quantum amplitude for the QPS process is exponentially small in the ratio E/E. At given magnetic flux, each QPS can be described as the tunneling of the phase difference of a single junction of almost 2?, accompanied by a small harmonic displacement of the phase difference of the other N-1 junctions. As a consequence, the total QPS amplitude ? is a global property of the ring. Here, we study the dependence of ? on the ring size N, taking into account the effect of a finite capacitance C to ground, which leads to the appearance of low-frequency dispersive modes. Josephson and charging effects compete and lead to a nonmonotonic dependence of the ring's critical current on N. For N->?, the system converges either towards a superconducting or an insulating state, depending on the ratio between the charging energy E=e2/2C and the Josephson coupling energy E. © 2013 American Physical Society.