Computational Modelling of Superconducting Quantum Interference Devices

Abstract

Superconducting quantum interference devices (SQUIDs) are state-of-the-art magnetic flux-to-voltage transducers with a plethora of applications spanning ultra-high precision magnetometry, medical imaging, remote sensing and quantum metrology. Several figures-of-merit have been devised to assess the performance of a SQUID for sensing applications. These descriptors allow for an objective ranking of the sensing capabilities of different devices. An open problem in the discipline is concerned with the optimisation of SQUIDs relative to these performance criteria. While the optimisation process could be carried out via an iterative cycle of design, fabrication and measurement, where the results yielded from one set of devices serves to inform future designs, this process is time-consuming and cost-prohibitive. An alternative method is to develop a mathematical model that is able to accurately describe the behaviour of SQUIDs and perform the optimisation process computationally using the wealth of available global optimisation algorithms. The goal of this research is to develop a core framework that is capable of modelling an arbitrary superconducting device, using the specified design parameters of the device together with relevant material parameters as inputs to the model. This work builds upon existing models in the field, based upon a lumped element circuit model together with elementary superconducting theory. The model is capable of simulating noise, capacitive effects, temperature dependent parameter variation, asymmetry in the device, and also possesses the capacity to directly compute the loop inductances from the device geometry. The intention is to create a realistic model that is both lightweight and predictive, so that it is amenable for use in the computational search for an optimal device design. We validate our model by applying it to the direct current (DC) SQUID and the one-dimensional parallel superconducting quantum interference filter (SQIF), for which there are prior studies and experimental data available for comparison. We also perform an initial exploratory investigation of the influence of each of the device parameters on the characteristic behaviour of the SQUID and begin to place bounds on the region of parameter space in which the device is operating under a desirable regime, so as to restrict the regions that should be searched more intensively for an optimal configuration. The outcomes of this project will form the foundation of the design process of real superconducting devices to be carried out with supercomputing facilities, and will lead to future collaborations with foundries such as SEEQC where the model may be used to inform the development and fabrication of new, more performant devices.