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arXiv:cond-mat/0509729 · Physical Review B

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

Jeffrey E. Marchese, Matteo Cirillo, Niels Grønbech‐Jensen

Published May 10, 2006• 22 citations
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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 nonzero 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.

DOI
10.1103/physrevb.73.174507

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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 nonzero 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 study analytically and numerically the phase-modulation properties of a classical Josephson tunnel junction biased in the zero-voltage state and phase locked to an external ac field. We show that the phase-locked state is being modulated in the transients, or in response to perturbations, and the modulation frequency is calculated as a function of relevant system parameters, such as microwave field amplitude. Our analysis demonstrates that the modulation of a phase-locked state in an entirely classical Josephson junction produces oscillations analogous to quantum mechanical Rabi oscillations, expected to be observed under the same conditions.
We present an analytical and computational study of resonances and transient responses in a classical Josephson junction system. A theoretical basis for resonances in a superconducting loop with three junctions is presented, outlining both the direct relationship between the dynamics of single- and multijunction systems and the direct relationships between observations of the classical counterparts to Rabi oscillations, Ramsey fringes, and spin-echo oscillations in this class of systems. We show simulation data along with analytical analyses of the classical model, and the results are related to previously reported experiments conducted on three junction loops. We further investigate the effect of off-resonant microwave perturbations to, e.g., the Rabi-type response of the Josephson system, and we relate this response back to the nonlinear and multivalued resonance behavior previously reported for a single Josephson junction. The close relationships between single and multijunction behaviors demonstrate the underlying dynamical mechanism for a whole class of classical counterparts to expected quantum-mechanical observations in a variety of systems, namely, the resonant and transient behavior of a particle in an anharmonic potential well with subsequent escape.
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.
We investigate, by experiments and numerical simulations, thermal activation processes of Josephson tunnel junctions in the presence of microwave radiation. When the applied signal resonates with the Josephson plasma frequency oscillations, the switching current may become multivalued in a temperature range far exceeding the classical to quantum crossover temperature. Plots of the switching currents traced as a function of the applied signal frequency show very good agreement with the functional forms expected from Josephson plasma frequency dependencies on the bias current. Throughout, numerical simulations of the corresponding thermally driven classical Josephson junction model show very good agreement with the experimental data.
We consider a Josephson junction coupled to a high-quality parallel resonance circuit under microwave irradiation on the resonance frequency. The phase locking of Josephson oscillations, manifesting itself through Shapiro steps, is studied using an analytical theory developed for the circuit. Substantial change in the amplitude of the oscillating component of the Josephson phase within the phase-locking range determines specificity of the step behavior. This analysis is compared with the results of a numerical simulation.