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Physics Letters A

Quantum electrodynamic engineering consequences of the weak link critical voltage law

A. Widom, Terrence D. Clark

Published Dec 1, 1983• 3 citations
Publisher
DOI
10.1016/0375-9601(83)90903-9

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The quantum phase-coherent behavior of superconducting weak links (WLs) is often quenched in the finite voltage state, due to the heat dissipation and related thermal hysteresis. The latter can be reduced by improving heat evacuation and/or by lowering the critical current so a phase-dynamic regime is obtained, albeit over a narrow bias-current and temperature range. Here we demonstrate that an inductive shunt with well-chosen parameters introduces unexpected nonlinear dynamics that destabilize an otherwise stable fixed point in the dissipative branch. This leads to a nonhysteretic behavior with large voltage oscillations in intrinsically hysteretic WL-based micron-size superconducting quantum interference devices. A dynamic thermal model quantitatively describes our observations and further allows us to elaborate on the optimal shunting conditions.

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We consider a superconducting loop with two weak links that encloses a magnetic flux. The weak links are unequal and are treated as Josephson junctions with non-sinusoidal phase dependence. We devise a model that takes into account the fluctuation of the critical currents, due to the fluctuations of the order parameter in the weak links. These fluctuations are important near the onset of superconductivity; in this regime they may significantly weaken and eventually disconnect the superconducting loop. As a consequence of these fluctuations and of the resistive noise in the junctions, the average dc voltage does not vanish. Our model can be easily extended to provide a qualitative description of a recent experiment.
Starting with a simple Lagrangian for the electromagnetic field with broken gauge symmetry, we derive an effective circuit Hamiltonian for a superconducting weak-link ring. The energy eigenstates of this Hamiltonian exhibit sensitivity to both external magnetic flux and an applied Faraday law voltage. We show that the flux periodicity of the rf SQUID ring, and the voltage periodic behaviour found in ultra-small-capacitance weak-link rings, can be seen as limiting cases of a more general phenomenon.
The quantum phase-coherent behavior of superconducting weak links (WLs) is often quenched in the finite voltage state, due to the heat dissipation and related thermal hysteresis. The latter can be reduced by improving heat evacuation and/or by lowering the critical current so a phase-dynamic regime is obtained, albeit over a narrow bias-current and temperature range. Here we demonstrate that an inductive shunt with well-chosen parameters introduces unexpected nonlinear dynamics that destabilize an otherwise stable fixed point in the dissipative branch. This leads to a nonhysteretic behavior with large voltage oscillations in intrinsically hysteretic WL-based micron-size superconducting quantum interference devices. A dynamic thermal model quantitatively describes our observations and further allows us to elaborate on the optimal shunting conditions.