A Classical Analysis of Capacitively Coupled Superconducting Qubits

An electrical circuit consisting of two capacitively coupled inductive loops, each interrupted by a Josephson junction, is analyzed through the classical RSCJ model. The same circuit has recently been studied experimentally and the results were used to demonstrate quantum mechanical entanglement in the system by observing the correlated states of the two inductive loops after initial microwave perturbations. Our classical analysis shows that the observed phenomenon exists entirely within the classical RSCJ model, and we provide a detailed intuitive description of the transient dynamics responsible for the observations.