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InTech eBooks

Effective Models of Superconducting Quantum Interference Devices

R. De

Published Oct 17, 2012• 0 citations
Publisher

Abstract

It is well known that the electrodynamic properties of SQUIDs (Superconducting Quantum Interference Devices) are obtained by means of the dynamics of the Josephson junctions in these superconducting system (Barone & Paterno, 1982; Likharev, 1986; Clarke & Braginsky, 2004). Due to the intrinsic macroscopic coherence of superconductors, r. f. SQUIDs have been proposed as basic units (qubits) in quantum computing (Bocko et al., 1997). In the realm of quantum computing non-dissipative quantum systems with small (or null) inductance parameter and finite capacitance of the Josephson junctions (JJs) are usually considered (Crankshaw & Orlando, 2001). The mesoscopic non-simply connected classical devices, on the other hand, are generally operated and studied in the overdamped limit with negligible capacitance of the JJs and small (or null) values of the inductance parameter. Nonetheless, r. f. SQUIDs find application in a large variety of fields, from biomedicine to aircraft maintenance (Clarke & Braginsky, 2004), justifying actual scientific interest in them.

DOI
10.5772/48483

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It is well known that the electrodynamic properties of SQUIDs (Superconducting Quantum Interference Devices) are obtained by means of the dynamics of the Josephson junctions in these superconducting system (Barone & Paterno, 1982; Likharev, 1986; Clarke & Braginsky, 2004). Due to the intrinsic macroscopic coherence of superconductors, r. f. SQUIDs have been proposed as basic units (qubits) in quantum computing (Bocko et al., 1997). In the realm of quantum computing non-dissipative quantum systems with small (or null) inductance parameter and finite capacitance of the Josephson junctions (JJs) are usually considered (Crankshaw & Orlando, 2001). The mesoscopic non-simply connected classical devices, on the other hand, are generally operated and studied in the overdamped limit with negligible capacitance of the JJs and small (or null) values of the inductance parameter. Nonetheless, r. f. SQUIDs find application in a large variety of fields, from biomedicine to aircraft maintenance (Clarke & Braginsky, 2004), justifying actual scientific interest in them.
It is necessary to miniaturize inductors for large-scale integration of Josephson devices. Utilizing the equivalent inductance of Josephson junctions is one promising method to realize small inductors. In this paper we calculate the static characteristics of some superconducting quantum interference devices (SQUIDs) utilizing the equivalent inductance, and we compare the results with those of SQUIDs employing the normal inductors. We also discuss the current distribution before and after the transition of the gate junctions. © 1998 Scripta Technica, Electron Comm Jpn Pt 2, 81(6): 1–7, 1998
Quantum mechanics and superconductivity are intimately connected on many levels. Quantum mechanics is needed to understand why a metal is a metal. The BCS condensate of Cooper pairs would not exist without quantum mechanics, nor could Cooper pairs tunnel through the barriers of Josephson junctions. The name SQUID is the abbreviation of superconducting quantum interference device. Yet another level of quantumness has been added in the last two decades. It turns out to be possible to design and fabricate superconducting objects that have macroscopic dimensions and properties, but behave as if they are single quantum particles. Amplitude and phase of the superconducting wavefunction act as conjugate quantum variables. Practical devices and circuits make use of Josephson junctions to reach the parameter values that are needed, but there is a clear distinction from the Josephson electronics circuits in the other chapters of this book. The latter may, in this context, well be referred to as being classical.
Nanoscale superconducting quantum interference devices (nano-SQUIDS) where the weak links are made from nanobridges, i.e., nanobridge SQUIDs (NBSs), are one of the most sensitive magnetometers for nanoscale magnetometry. Because of very strong nonlinearity in the nanobridge-electrode joints, the applied magnetic flux (${\mathrm{\ensuremath{\Phi}}}_{a}$)--critical current (Ic{I}_{c}Ic​) characteristics of NBSs differ very significantly from conventional tunnel-junction SQUIDs, especially when the nanobridges are long and/or the screening parameter is large. However, in most of the theoretical descriptions, NBSs have been treated as the conventional tunnel-junction SQUIDs, which are based on the dc Josephson effect. Here, I present a model demonstrating that for long nanobridges and/or large screening parameters the ${I}_{c}({\mathrm{\ensuremath{\Phi}}}_{a})$ of a NBS can be explained by merely considering the fluxoid quantization in the NBS loop and the energy of the NBS; it is not necessary to take the Josephson effect into consideration. I also demonstrate that using the model, one can derive useful expressions such as the modulation depth and transfer function. I discuss the role of the kinetic inductance fraction ($\ensuremath{\kappa}$) in determining ${I}_{c}({\mathrm{\ensuremath{\Phi}}}_{a})$. I compare the predictions of the present model with the experimental data already published by several groups.
The dynamic properties of a superconducting quantum interference device (SQUID) containing arrays of Josephson junctions in a superconducting loop, and in particular the case of a four-junction SQUID, is analyzed theoretically via computer simulations. It is shown that phase locking of Josephson junctions determines the dynamic behavior of the SQUID. In the case of a stable phase-lock state hysteretic I-V curves as well as unusual voltage-flux dependencies appear. The influence of a small spread in the Josephson junction parameters upon the stability of the phase-lock state is investigated in parameter space.
We study several parasitic effects on the implementation of a Josephson radiation comb generator based on a dc superconducting quantum interference device (SQUID) driven by an external magnetic field. This system can be used as a radiation generator similarly to what is done in optics and metrology, and allows one to generate up to several hundreds of harmonics of the driving frequency. First we take into account how the assumption of a finite loop geometrical inductance and junction capacitance in each SQUID may alter the operation of the devices. Then, we estimate the effect of imperfections in the fabrication of an array of SQUIDs, which is an unavoidable source of errors in practical situations. We show that the role of the junction capacitance is, in general, negligible, whereas the geometrical inductance has a beneficial effect on the performance of the device. The errors on the areas and junction resistance asymmetries may deteriorate the performance, but their effect can be limited to a large extent by a suitable choice of fabrication parameters.
In Chapter 2 we made use of a hypothetical arrangement of a strongly coupled superconducting ring, interrupted by a region of weak superconductivity, to derive the essential features of the Josephson effects. In practice this same arrangement is actually employed as the basis of one of the most useful superconducting devices developed so far, the single-junction, or rf, squid . (As mentioned in the Introduction, squid is an acronym for Superconducting QUantum Interference Device.) Here the essential physics behind the operation of these important devices will be described, and in the following section the practical realisation of an rf squid with its associated readout electronics will be explained. Chapter 4 will treat in a similar way dc squid s, which are related devices possessing two weak links in a single ring, whose mode of operation is rather different.