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IEEE International Superconductive Electronics Conference (ISEC)

Bi-SQUID noise simulation

Aleksei Sharafiev, Victor K. Kornev, Igor I. Soloviev, Oleg A. Mukhanov

Published Jul 1, 2013• 1 citation
Publisher

Abstract

We present an analysis of noise characteristics of bi-SQUID through its voltage response and compare to characteristics of dc SQUID in the open loop configuration. The additional Josephson junction in bi-SQUID gives an additional source of fluctuations, changes transfer function, nonlinear dynamics and nonlinear noise spectrum transformation. These result in different input noise level versus applied magnetic flux.

DOI
10.1109/isec.2013.6604308

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We present an analysis of noise characteristics of bi-SQUID through its voltage response and compare to characteristics of dc SQUID in the open loop configuration. The additional Josephson junction in bi-SQUID gives an additional source of fluctuations, changes transfer function, nonlinear dynamics and nonlinear noise spectrum transformation. These result in different input noise level versus applied magnetic flux.
We present an improved analytic theory, numerical simulation, and analysis of noise characteristics of a bi-SQUID in comparison with those of a dc SQUID in an open loop configuration. The analytic theory which had been developed earlier, neglecting a pulse component of the difference of the phases of Josephson junctions, is now completed taking into account the pulse component. In the bi-SQUID, the additional Josephson junction introduces another source of fluctuations and changes its transfer function, nonlinear dynamics, and the noise spectrum transformation. Some increase in the reduced-to-input noise at low values of applied magnetic flux comes from the nonlinear flux to phase difference transformation that was introduced in bi-SQUID as a way to linearize its voltage response.
The noise characteristics at low frequencies are studied for various planar dc SQUIDs made of junctions with different barrier materials of a-Si, aluminum oxide, and niobium oxide. It is found that fluctuations of the parameters of individual junctions contribute to the flux noise of the SQUIDs in a magnitude of the same order with the apparent flux noise. The magnitude of the flux noise due to the parameter fluctuations depends on the barrier material and on the inductance parameter βL . We have observed a telegraph noise in the voltage time trace and a Lorentzian in the voltage power spectrum for a current-biased SQUID. As a source of the parameter fluctuations, capture and emission of electrons at the trapping sites in the barrier are indicated.
The current noise circulating around the loop of a tunnel junction dc SQUID has been measured as a function of applied flux. The flux noise generated by this current was coupled via a superconducting transformer to a second dc SQUID that was used to measure the noise in a null-balancing configuration. The voltage noise across the SQUID was also measured, using a cooled LC-resonant circuit, and the correlation between the voltage and current noises was determined. The measured values of the noises are in good agreement with values obtained from an analog simulator.
We have fabricated Y1Ba2Cu3O7−x step-edge junction dc superconducting quantum interference devices (SQUIDs) and characterized their noise performance. The current-voltage characteristics of our SQUIDs are of resistively shunted junction type with critical current densities jc of about 104 A/cm2 and maximum flux to voltage transfer functions δV/δΦ of 20 μV/Φ0 at 77 K. We compare model predictions for 1/f noise in dc SQUIDs with experimental data and show that the frequency dependent noise in our devices results from critical current fluctuations of the Josephson junctions. A bias current reversing technique is effective in suppressing this noise contribution. A flux noise Φn of 80 μΦ0/Hz1/2 at 1 Hz and 77 K was measured on a dc SQUID with an inductance Ls of 60 pH.
We show that the voltage response of a dc SQUID can be substantially linearized by the introduction of a nonlinear inductance. The inductance tuning allows us to achieve response linearity close to 120 dB. Such a nonlinear inductance can be easily formed using Josephson junction inductance. The additional junction and main inductance form a single-junction SQUID and hence the device can be called a bi-SQUID. To obtain high dynamic range commensurate to the high response linearity, one can use a serial array of nonlinear inductance dc SQUIDs. Experimental studies of a single bi-SQUID and serial arrays of bi-SQUIDs are reported and discussed.
The flux noise in a long superconducting quantum interference device (SQUID) array consisting of at least 100 dc-SQUID elements connected in series was characterized analytically, and then compared with measurements. In the analysis, noise sources in the array were shunt resistors for Josephson junctions, a damping resistor for a SQUID loop, the dynamic resistance of the SQUID array, and the noise of electronics at room temperature. The flux noise of the array was calculated analytically as a function of the number of dc-SQUID elements. The results reveal that the flux noise is significantly influenced by the dynamic resistance of the array, although the influence by the dynamic resistance for a single SQUID is negligibly small. The dynamic resistance becomes dominant for the flux noise when the number of SQUID elements in the array exceeds 100. These results agree well with the measured flux noise for a long SQUID array constructed using a Nb/AlO x /Nb fabrication process.