Quantum dynamics of a 4π kink in Josephson junction parallel arrays with large kinetic inductance

Abstract

We present a theoretical study of the quantum dynamics of two magnetic fluxons trapped in Josephson junction parallel arrays (JJPAs) with large kinetic inductances. The Josephson phase distribution of two trapped magnetic fluxons satisfies a topological constraint, i.e., the total variation of Josephson phases along a JJPA is $4\ensuremath{\pi}$. In such JJPAs the characteristic length of the Josephson phase distribution (``the size'' of magnetic fluxon) is drastically reduced to be less than a single cell size. Two extreme dynamic patterns will be distinguished: two weakly interacting and two merged magnetic fluxons, i.e., a $4\ensuremath{\pi}$ kink. Taking into account the repulsive interaction between two magnetic fluxons located in the same or adjacent cells, we obtain the energy band spectrum ${E}_{4\ensuremath{\pi}}(p)$ for a quantum $4\ensuremath{\pi}$ kink. The coherent quantum dynamics of $4\ensuremath{\pi}$ kinks demonstrates the quantum beats with the frequency and amplitude strongly deviating from those observed for two independent magnetic fluxons. In the presence of applied dc and ac bias currents of frequency $f$ a weakly incoherent quantum dynamics of a $4\ensuremath{\pi}$ kink results in the Bloch oscillations and the seminal current steps with values ${I}_{4\ensuremath{\pi}}^{(n)}=enf$ which are two times less than those for two independent magnetic fluxons.