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

TL;DR

This paper provides a classical analytical framework for understanding phase-locking transients and Rabi-type oscillations in microwave-driven Josephson junctions, linking transient modulation to switching probabilities and matching simulations with experimental data.

Contribution

It introduces a perturbation method that yields closed-form analytical results for modulation attenuation and oscillation frequency, expanding previous classical analyses of Josephson junction dynamics.

Findings

Transient low-frequency modulation correlates with switching probability.

Analytical results match numerical simulations and experimental data.

Phase-locking transients are closely related to observed Rabi-type oscillations.

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.