We analyze the coherent dynamics of a fluxonium device (Manucharyan et al 2009 Science 326 113) formed by a superconducting ring of Josephson junctions in which strong quantum phase fluctuations are localized exclusively on a single weak element. In
such a system, quantum phase tunnelling by $2pi $ occurring at the weak element couples the states of the ring with supercurrents circulating in opposite directions, while the rest of the ring provides an intrinsic electromagnetic environment of the qubit. Taking into account the capacitive coupling between nearest neighbors and the capacitance to the ground, we show that the homogeneous part of the ring can sustain electrodynamic modes which couple to the two levels of the flux qubit. In particular, when the number of Josephson junctions is increased, several low-energy modes can have frequencies lower than the qubit frequency. This gives rise to a quasiperiodic dynamics, which manifests itself as a decay of oscillations between the two counterpropagating current states at short times, followed by oscillation-like revivals at later times. We analyze how the system approaches such a dynamics as the rings length is increased and discuss possible experimental implications of this non-adiabatic regime.
We study quantum phase-slip (QPS) processes in a superconducting ring containing N Josephson junctions and threaded by an external static magnetic flux. In a such system, a QPS consists of a quantum tunneling event connecting two distinct classical s
tates of the phases with different persistent currents [K. A. Matveev et al., Phys. Rev. Lett. 89, 096802 (2002)]. When the Josephson coupling energy EJ of the junctions is larger than the charging energy EC = e2/2C where C is the junction capacitance, the quantum amplitude for the QPS process is exponentially small in the ratio EJ/EC. At given magnetic flux each QPS can be described as the tunneling of the phase difference of a single junction of almost 2pi, accompanied by a small harmonic displacement of the phase difference of the other N-1 junctions. As a consequence the total QPS amplitude nu is a global property of the ring. Here we study the dependence of nu on the ring size N taking into account the effect of a finite capacitance C0 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 critical current on N. For N=infty, the system converges either towards a superconducting or an insulating state, depending on the ratio between the charging energy E0 = e2/2C0 and the Josephson coupling energy EJ.
