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AIP conference proceedings

Non-adiabatic phenomena in a coupled SQUID ring-tank circuit system in the strongly hysteretic regime

Helen Prance

Published Jan 1, 2000• 0 citations
Publisher

Abstract

In this paper we consider new and remarkable dynamical behavior displayed by a strongly hysteretic SQUID (Superconducting QUantum Interference device)-a single Josephson weak link enclosed by a thick superconducting ring inductively coupled to a radio frequency (rf) parallel LC tank circuit resonator. Experimentally, we show that in the strongly hysteretic regime this coupled system can display remarkable level structure in its dynamics, quite different to that normally associated with rf driven SQUID ring systems. We demonstrate theoretically that this level structure arises when the SQUID ring responds non-adiabatically to time dependent changes in its potential, i.e. so that the ring no longer stays at or very close to the minimum in this potential as it changes in time.

DOI
10.1063/1.1302438

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In this paper we consider new and remarkable dynamical behavior displayed by a strongly hysteretic SQUID (Superconducting QUantum Interference device)-a single Josephson weak link enclosed by a thick superconducting ring inductively coupled to a radio frequency (rf) parallel LC tank circuit resonator. Experimentally, we show that in the strongly hysteretic regime this coupled system can display remarkable level structure in its dynamics, quite different to that normally associated with rf driven SQUID ring systems. We demonstrate theoretically that this level structure arises when the SQUID ring responds non-adiabatically to time dependent changes in its potential, i.e. so that the ring no longer stays at or very close to the minimum in this potential as it changes in time.
In this article, we show that the radio frequency (rf) dynamical characteristics of a very strongly hysteretic superconducting quantum interference device (SQUID) ring, coupled to a rf tank circuit resonator, display relaxation oscillations. We demonstrate that the overall form of these characteristics, together with the relaxation oscillations, can be modeled accurately by solving the quasiclassical nonlinear equations of motion for the system. We suggest that in these very strongly hysteretic regimes, SQUID ring-resonator systems may find application in logic and memory devices.
In this paper we consider the modulation of a SQUID ring (a Josephson weak link enclosed by a thick superconducting ring) by an external electromagnetic (em) field for the case where the ring remains adiabatically in its ground state. We demonstrate that very good agreement can be found between experimental modulation data and the results predicted theoretically by solving the time-dependent Schrödinger equation for the ring-em-field system. We also show that the non-linear dynamical coupling between the ring and an external resonant circuit can influence the exact form of the modulation. Again we find consistent agreement between experiment and theory.
In this paper we study numerical solutions to the quasiclassical equations of motion for a superconducting-quantum-interference device ring-radio frequency (rf) resonator system in the regime where the ring is highly hysteretic. In line with experiment, we show that for a suitable choice of ring circuit parameters the solutions to these equations of motion comprise sets of levels in the rf voltage-current dynamics of the coupled system. We further demonstrate that transitions, both up and down, between these levels can be controlled by voltage pulses applied to the system, thus opening up the possibility of high order (e.g., 10 state), multilevel logic and memory.
Conventional rf SQUIDs (superconducting quantum interference devices) consist of a superconducting loop interrupted by one weak link, and when read out via a tank circuit they produce output signals in the order of a few tens of microvolts. When the single weak link is replaced by a dc SQUID (a superconducting loop with two junctions) a so-called double quantization loop SQUID is formed. In this paper it is shown theoretically, and supported experimentally with thin-film devices of three different designs, that the general behaviour can be explained by a simplified picture of the fixed critical current of the single junction of the rf SQUID being replaced by an effective critical current of a dc SQUID loop that is varied by the applied magnetic flux (i.e., we have a rf SQUID with a variable β parameter). A more detailed analysis of the experimental data and the theory of this novel device reveals its interesting nonlinear character and shows the deviations from this simple picture. It is demonstrated experimentally that output signals in the order of ≥1 mV can be obtained with a suitable read-out mode for the tank circuit, a clear advantage when compared to conventional rf SQUIDs. With respect to dc SQUIDs, the coupling to integrated planar input coils will be unproblematic since no microwave resonances should occur in the structures.
Based on the hypothesis that the macroscopic superconducting shielding current on the surface of a porous granular superconductor is short lived due to the action of thermal noise, a dispersive-mode theory for a high-temperature radio-frequency superconducting quantum interference device (rf SQUID) is suggested. In this theory, the effect of the SQUID ring on the resonant tank circuit is an effective inductance Le{L}_{e}Le​, Le{L}_{e}Le​=k2{k}^{2}k2FLT{\mathrm{FL}}_{T}FLT​, where k is the coupling coefficient between the SQUID ring and the resonant tank circuit with inductance LT{L}_{T}LT​, and F is a periodic function of external flux ${\ensuremath{\Phi}}_{\mathrm{dc}}$ with a period of flux quantum ${\ensuremath{\Phi}}_{0}$. The phenomena that the weak-link-rf-SQUID flux-receiving area defined by the hole of the SQUID ring and the bulk-rf-SQUID flux-receiving area, which is determined by an annular surface region with a thickness of the effective penetration depth ${\ensuremath{\lambda}}_{e}$, can be interpreted. The theory is qualitatively consistent with available experimental results.