Classical analysis of phase-locking transients and Rabi-type oscillations in microwave-driven Josephson junctions

Abstract

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.

Nonequilibrium transient phenomena in the washboard potential

“…The results presented above rely on the fact that specific initial conditions imposed at the initiation of each sweep of the escape process out of a Josephson junction washboard potential give rise to underdamped oscillations. These oscillations survive coherently throughout the sweep until the switching event takes place, similar to other reported cases [2,20]. We presume that these oscillations are generated by an initial perturbation due to temperature, or recurring cycling of the current sweeps or the perturbation from the onset of the bias sweep itself.…”

A survey of classical and quantum interpretations of experiments on Josephson junctions at very low temperatures

“…The numerical simulations had shown striking agreement with experimental reality and analytical approaches for ac driven junctions. Thus, three years after the appearance of Martinis and co-workers' paper on the Rabi oscillations, papers were published [48,49] in which it was shown that the features reported in the Martinis Rabi paper could be well interpreted by the nonlinear phenomenology of Josephson junctions. The analytical approximations were in striking agreement with numerical simulations and the experimental results [45,50] as revealed in the lower panel of Fig.35, and by the comparison between analytical ansatz, numerical simulation and experiments shown in Fig.36.…”

Magnetic reversal dynamics of a quantum system on a picosecond timescale

“…It is important to pay attention to this profound analogy between the quantum and the classical results in order to separate the macroscopic and quantum modes in mesoscopic systems, which is often a difficult task [ 41 – 42 ]. Moreover, it seems promising to simulate the behavior of magnetic metamaterials based on artificial Josephson atoms in sufficiently strong fields [ 43 ] using standard classic software designed to study the magnetization reversal processes in large magnetic clusters [ 44 ].…”