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Acta Physica Polonica A

Self-Induced Resonances in Asymmetric Superconducting Quantum Interference Devices

T. P. Polak, E. Sarnelli

Published Jul 1, 2008• 0 citations
Publisher

Abstract

Theory of self-induced resonances in asymmetric two-junction interferometer device is presented.An extension of previous theoretical approaches contains inclusions from several asymmetries: the Josephson current , capacitances χ and dissipation ρ presented in an equivalent circuit.Our theory can be useful to determine asymmetry parameters always present in lightly damped asymmetric SQUIDs made from low-and high-T C materials.

DOI
10.12693/aphyspola.114.203

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Theory of self-induced resonances in asymmetric two-junction interferometer device is presented.An extension of previous theoretical approaches contains inclusions from several asymmetries: the Josephson current , capacitances χ and dissipation ρ presented in an equivalent circuit.Our theory can be useful to determine asymmetry parameters always present in lightly damped asymmetric SQUIDs made from low-and high-T C materials.
The theory of self-induced resonances in asymmetric two-junction interferometer device is presented. In real devices, it is impossible to have an ideal interferometer free of imperfections. Thus, we extended previous theoretical approaches, introducing a model that contains several asymmetries: Josephson current ϵϵϵ, capacitances $\ensuremath{\chi}$, and dissipation $\ensuremath{\rho}$ presented in an equivalent circuit. Moreover, nonconventional symmetry of the order parameter in high temperature superconducting quantum interference devices forced us to include phase asymmetries. Therefore, the model has been extended to the case of $\ensuremath{\pi}$-shift interferometers, where a phase shift is present in one of the junctions.
The LC\mathrm{LC}LC (inductance-capacitance) resonance phenomenon in the dc SQUID (superconducting quantum interference device) creates a current peak in the $I\ensuremath{-}V$ characteristics at a voltage determined by the resonance frequency. These $I\ensuremath{-}V$ characteristics have been analyzed with the resistively shunted Josephson-junction model in the low-damping and small-oscillation regime. The resonance $I\ensuremath{-}V$ characteristics contain sufficient information to determine all circuit parameters for the dc SQUID's. Specifically, we can apply this analysis to symmetric, tunnel-junction dc SQUID's to deduce the pair-quasiparticle interference conductance ($cos\ensuremath{\theta}$ term).
Direct current-superconducting quantum interference devices (SQUIDs) characterized by asymmetric Josephson junctions have never been used for applications. In order to demonstrate their potential advantages, a throughout numerical analysis of different asymmetric configurations has been carried out. A damping resistance has been included in the SQUID circuit and the thermal noise associated with junction and damping resistances has been considered in the numerical model. Magnetic modulations and flux noise spectral densities have been computed as a function of many parameters (bias current, asymmetry, SQUID inductance, and damping resistance) and the performance of symmetric and asymmetric devices have been compared. The results show that, by properly optimizing the SQUID design, asymmetric SQUIDs are characterized by higher magnetic flux to voltage transfer coefficient and lower flux noise. As a result, asymmetric configurations can be very useful in all the applications where high sensitivity is required.
An analytical approach that makes it possible to reconstruct the current–phase relation (CPR) in Josephson structures included in one of the arms of a two-junction superconducting quantum interference device (SQUID), where the second junction has a significantly higher critical current and a known (sinusoidal) CPR, has been developed. The developed methods of analytical and numerical studies of current–flow transformations in two-junction SQUIDs make it possible to reconstruct the CPR of a junction with a low critical current taking into account both the existence of the self-inductance of the interferometer contour and a possible asymmetry in the supply current system. The efficiency of this approach has been confirmed by the experimental study of niobium–aluminum/aluminum oxide–niobium test structures with the known CPR.
Direct current superconducting quantum interference devices made by Josephson junctions with asymmetric shunt resistances have been numerically investigated in the low temperature regime. When combined with a damping resistance, the asymmetry leads to a flux to voltage transfer coefficient several times larger than the one typical of symmetric devices, together with a lower magnetic flux noise. These results show that this type of asymmetric device may replace the standard ones in a large number of magnetometric applications, improving the sensitivity performance. The large transfer coefficient may also simplify the readout electronics allowing a direct coupling of asymmetric devices to an external preamplifier, without the need of an impedance matching flux transformer.
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.