An electrical circuit consisting of two capacitively coupled inductive loops, each interrupted by a Josephson junction, is analyzed through the classical resistively and capacitively shunted junction ͑RCSJ͒ model. The same circuit has recently been studied experimentally and the results were used to demonstrate quantummechanical 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 RCSJ model, and we provide a detailed intuitive description of the transient dynamics responsible for the observations.

We present a classical analysis of the transient response of Josephson junctions perturbed by microwaves and thermal fluctuations. The results include a specific low frequency modulation in phase and amplitude behavior of a junction in its zero-voltage state. This transient modulation frequency is linked directly to an observed variation in the probability for the system to switch to its non-zero voltage state. Complementing previous work on linking classical analysis to the experimental observations of Rabi-oscillations, this expanded perturbation method also provides closed form analytical results for attenuation of the modulations and the Rabi-type oscillation frequency. Results of perturbation analysis are compared directly (and quantitatively) to numerical simulations of the classical model as well as published experimental data, suggesting that transients to phase-locking are closely related to the observed oscillations.

We investigate the results of recently published experiments on the quantum behavior of Josephson circuits in terms of the classical modelling based on the resistively and capacitivelyshunted (RCSJ) junction model. Our analysis shows evidence for a close analogy between the nonlinear behavior of a pulsed microwave-driven Josephson junction at low temperature and low dissipation and the experimental observations reported for the Josephson circuits. Specifically, we demonstrate that Rabi-oscillations, Ramsey-fringes, and spin-echo observations are not phenomena with a unique quantum interpretation. In fact, they are natural consequences of transients to phase-locking in classical nonlinear dynamics and can be observed in a purely classical model of a Josephson junction when the experimental recipe for the application of microwaves is followed and the experimental detection scheme followed. We therefore conclude that classical nonlinear dynamics can contribute to the understanding of relevant experimental observations of Josephson response to various microwave perturbations at very low temperature and low dissipation.

We provide an alternative interpretation of experimental results that were represented as demonstrating entanglement between two macroscopic quantum Josephson oscillators. We model the experimental system using the well-established classical equivalent circuit of a resistively and capacitively shunted Josephson junction. Simulation results are used to generate the corresponding density matrix which shows features quite similar to the previously published matrix generated from experimental data. Since our data are generated by a classical model, we therefore submit that state tomography cannot be used to determine absolutely whether or not quantum entanglement has taken place. Analytical arguments are given for why the classical analysis provides an adequate explanation of the experimental results.

We present evidence for a close analogy between the nonlinear behaviour of a pulsed microwave-driven Josephson junction at low temperature and the experimentally observed behaviour of Josephson systems operated below the quantum transition temperature under similar conditions. We specifically address observations of Ramsey-type fringe oscillations, which can be understood in classical nonlinear dynamics as results of slow transient oscillations in a pulsed microwave environment. Simulations are conducted to mimic experimental measurements by recording the statistics of microwave-induced escape events from the anharmonic potential well of a zero-voltage state. Observations consistent with experimentally obtained Ramsey-type oscillations are found in the classical model.