Resonance phenomena in the annular array of underdamped Josephson junctions

The appearance and origin of resonance phenomena are studied in an annular system of underdamped Josephson junctions. If no fluxon is trapped in the system, the dynamics is governed by the motion of fluxon-antifluxon pairs. If, on the other hand, trapped fluxons are present, in addition to their motion, the system can also exhibit the simultaneous motion of trapped fluxons and fluxon-antifluxon pairs. Locking between the rotating excitations (fluxons and antifluxons) and the Josephson frequency leads to the appearance of zero-field steps in the current-voltage characteristics, whose number is determined by the number of junctions and the total number of excitations present in the system. The obtained results clearly show that the branching of zero-field steps due to resonance between the rotating excitations and plasma oscillations in their tails appears only at the lower steps and completely disappears at the higher steps. A comparative analysis between systems without and those with trapped fluxons shows a correlation between their current-voltage characteristics. From a high-resolution analysis some special features of zero-field steps emerge such as an additional branch due to resonance between the pulsating fluxon and the Josephson frequency. Examination of systems with the same number but different types of excitations further reveals that their dynamics is determined not only by the number, but also by the type of excitations, i.e., systems with the same number but different types of excitations have different current-voltage characteristics. © 2020 American Physical Society.