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AIP conference proceedings

Coupled Serial and Parallel Non-uniform SQUIDs

Patrick Longhini, Susan A. E. Berggren, Antonio Palacios, Anna Leese de Escobar, Visarath In, Visarath In, Antonio Palacios, Patrick Longhini

Published Jan 1, 2011• 0 citations
Publisher

Abstract

In this work we numerical model series and parallel non‐uniform superconducting quantum interference device (SQUID) array. Previous work has shown that series SQUID array constructed with a random distribution of loop sizes, (i.e. different areas for each SQUID loop) there exists a unique ‘anti‐peak’ at the zero magnetic field for the voltage versus applied magnetic field (V‐B). Similar results extend to a parallel SQUID array where the difference lies in the arrangement of the Josephson junctions. Other system parameter such as bias current, the number of loops, and mutual inductances are varied to demonstrate the change in dynamic range and linearity of the V‐B response. Application of the SQUID array as a low noise amplifier (LNA) would increase link margins and affect the entire communication system. For unmanned aerial vehicles (UAVs), size, weight and power are limited, the SQUID array would allow use of practical ‘electrically small’ antennas that provide acceptable gain.

DOI
10.1063/1.3586221

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In this work we numerical model series and parallel non‐uniform superconducting quantum interference device (SQUID) array. Previous work has shown that series SQUID array constructed with a random distribution of loop sizes, (i.e. different areas for each SQUID loop) there exists a unique ‘anti‐peak’ at the zero magnetic field for the voltage versus applied magnetic field (V‐B). Similar results extend to a parallel SQUID array where the difference lies in the arrangement of the Josephson junctions. Other system parameter such as bias current, the number of loops, and mutual inductances are varied to demonstrate the change in dynamic range and linearity of the V‐B response. Application of the SQUID array as a low noise amplifier (LNA) would increase link margins and affect the entire communication system. For unmanned aerial vehicles (UAVs), size, weight and power are limited, the SQUID array would allow use of practical ‘electrically small’ antennas that provide acceptable gain.
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Abstract Designing superconducting electronic devices involves a careful study of all the elements in the circuit, including the superconducting bias leads. In this work, we introduce a theoretical model for two-dimensional (2D) superconducting quantum interference device (SQUID) arrays capable of simulating the voltage-to-magnetic flux response of devices with different bias current configurations. First, we compare uniformly biased and centre biased SQUID arrays by investigating the voltage versus magnetic flux response, maximum transfer function and voltage modulation depth. Then, we calculate the time-averaged fluxoid distributions for one-dimensional (1D) and 2D centre biased arrays. Finally, we study the performance of the two bias current configurations depending on array size, screening parameter, thermal noise strength and kinetic self-inductance fraction. Our calculations reveal: (i) centre biased 1D parallel SQUID arrays present an unusual voltage response caused by the asymmetric fluxoid distribution; (ii) the optimal transfer function of centre biased arrays strongly depends on the number of junctions in parallel; (iii) the performance of centre biased arrays approaches the uniform biased ones when the number of junctions in series exceeds those in parallel; (iv) while the screening parameter and the thermal noise strength clearly affect the device performance, the kinetic to self-inductance fraction seems to play only a secondary role.
We present a theoretical study on the voltage response function 〈V〉 of series arrays of dc superconducting quantum interference devices (SQUIDs) for which the elementary dc SQUID loops vary in size and, possibly, in orientation. If the distribution of the array loop sizes is chosen according to an arithmetic relation, 〈V〉 is not a Φ0-periodic function of the strength of external magnetic field B. For arithmetic arrays the periodicity of 〈V〉 is controlled by the geometry of the array alone and does not depend on spreads in the array junction parameters. If small fluctuations are added to the loop size distribution, 〈V〉 becomes a unique function around a global minimum at B=0 without possessing significant additional minima for finite B. This filter property does not apply for conventional SQUIDs and series arrays of identical or nearly identical SQUID loops. Applications of arithmetic series arrays include the design of current amplifiers and novel quantum interference filters, which possess large voltage swing and low noise level. In particular, quantum interference filters should provide a rather simple and extremely sensitive measurement of the absolute strength of magnetic fields.
Arrays of dc-superconducting quantum interference devices (dc-SQUIDs) were investigated, in which each dc-SQUID element has a multiturn input coil. The dependence of flux noise on the number of turns of the input coil was studied for current amplifiers. SQUID arrays were fabricated by a Nb/AlO x /Nb Josephson tunnel junction fabrication process. Results show that the flux noise of the SQUID array amplifier does not depend on the turn number of the input coil. A SQUID array amplifier consisting of 128 dc-SQUID elements was fabricated, in which each element had a 7-turn input coil and a mutual inductance between the input coil and the SQUID loop of 460 pH. This amplifier showed an ultrahigh current resolution of 1 pA/Hz0.5 and a maximum input current of 11 µA for signals of 50 kHz, which is sufficient bandwidth for X-ray detection applications. These values correspond to a large dynamic range of 87 dB. The flux-voltage characteristics of this SQUID array, however, showed asymmetric behavior, which originated from electronic resonance in stray capacitance and the mutual inductance between the SQUID loop and the multiturn input coil.
A technique for the analysis of complex superconducting circuits containing one or more current biased inductively coupled Josephson junction interferometers is described. The equations of motion for the system are shown to separate into a set of non-linear junction equations relating the voltage drops across the junctions to the currents passing through the junctions, and a set of linear equations expressing the quantization of the fluxoid around the superconducting loops and the corresponding linear circuit equations for the normal loops. In many cases, the linear equations can be integrated, resulting in an effective elimination of the normal circuit loops from the problem. The circuit is thus reduced to that of an equivalent set of coupled SQUIDs whose device parameters are a function of the original circuit parameters and the inductive coupling strengths. The dc SQUID tuned linear amplifier is analyzed to display the method. As a result of this analysis, the optimal noise temperature of a tuned SQUID amplifier is derived as a function of the current and voltage noise spectral densities, Svand Sj, and forward transfer function, Vφ. The results obtained demonstrate that the behavior of the SQUID cannot be isolated from that of the rest of the circuit in the manner assumed in previous analyses. The existence of a quantum noise limit on the noise temperature of any phase preserving linear amplifier is used to infer that the noise figures must satisfy the constraint[(S_{v}/2LV_{\phi}^{2})(LS_{j}/2)-S_{vj}^{2}]^{1/2}>\hbarThe behavior of several simple circuits containing a pair of inductively coupled current biased interferometers is discussed to display the extension of the method to circuits containing more than one interferometer.
In this article, an all-NbN superconducting quantum interference device (SQUID) array was developed for future applications by taking advantage of the higher critical temperature of a NbN film compared with Nb. The NbN SQUID array was composed of 100 SQUIDs with equal loop areas connected in series. The array was fabricated on a single-crystal MgO (100) substrate using 3-μm-diameter NbN/AlN/NbN Josephson junctions. The hysteresis and shielding parameters of the SQUID were 0.67 and 0.15, respectively. The SQUIDs in the array were coherently modulated by injecting current in a common flux control line, which resulted in a modulation voltage of 3.54 mV with consistent periodicity and a flux-to-voltage transfer coefficient of 23 mV/Φ0. Using a flux locked loop circuit, the fabricated NbN SQUID array exhibited excellent performance with a low white flux noise of 1.4 μΦ0/√Hz, which included the preamplifier noise.