Capacitance-induced in-phase switching in a basic two-dimensional Josephson junction array

Phase locking in a basic two-dimensional Josephson junction array consisting of two coupled SQUIDs is studied exploiting a new method combining the ideas of harmonic balance with the phase-slip procedure. This permits not only including the effect of non-vanishing junction capacitance, but extending our earlier investigations of the same circuit to arbitrary ring inductances, including inductances l ≈ 1 as well. As a result, our earlier finding that only antiphase oscillations can be stable in such a circuit are modified by observing a transition to the in-phase regime for larger values of the junction capacitance. The transition between both regimes is found to be determined by the resonance condition between ring inductance and junction capacitance.