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Springer eBooks

Rabi Flopping and Coherent Transients in a Josephson Junction

Andrew L. DiRienzo, Daniel N. Rogovin, Marlan O. Scully

Published Jan 1, 1978• 0 citations
Publisher
DOI
10.1007/978-1-4757-0665-9_4

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Within the framework of the microscopic model of tunneling, we modeled the behavior of the Josephson junction shunted by the superconductor--insulator--normal-metal (SIN) tunnel junction. The electromagnetic impedance of the SIN junction includes both the frequency-dependent damping and reactance, which affect the circuit dynamics. We calculated the dc $I\text{\ensuremath{-}}V$ curves and transient characteristics and show their differences to the characteristics obtained within the simpler models. The correct operation of the basic single-flux-quantum circuits, i.e., the Josephson transmission line and the toggle flip-flop, based on such SIN-shunted Josephson junctions with small damping at low frequencies, has also been modeled.
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 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.