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Superconductor Science and Technology

Signal and noise characteristics of bi-SQUID

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

Published Oct 8, 2014• 26 citations
Publisher

Abstract

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.

DOI
10.1088/0953-2048/27/11/115009

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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 dynamics and noise of a dc SQUID (the Superconducting Quantum Interference Device), with the McCumber parameter /spl beta//sub c/=2/spl pi/R/sup 2/l/sub c/C//spl Phi//sub 0/ close to the unity (where I/sub c/, R, C is the critical current, the shunt resistance and the capacitance of the Josephson junctions comprising the SQUID, respectively, /spl Phi//sub 0/=2.07 10/sup -15/ Wb is the magnetic flux quantum) integrated with a planar spiral input coil, have been experimentally studied. The length of the spiral input coil was chosen so as to match its /spl lambda//4 microwave resonance frequency to the plasma resonance frequency of the SQUID. The input coil resonance is found to enhance the overall quality factor Q of the Josephson oscillations in the SQUID and, as a result, to increase the dynamic resistance R/sub d/ and the gradient of the flux-to-voltage characteristics, /spl delta/V//spl delta//spl Phi/, without hysteresis. A dc SQUID with a loop inductance L=30.5 pH, /spl beta//sub c/=0.72, and a 6 turn input coil demonstrated a non-distorted quasi-sinusoidal flux-to-voltage transfer function with an exceptionally large modulation depth of 140 /spl mu/V peak-to-peak. The spectral density of the magnetic flux noise was as low as 3.5/spl times/10/sup -7/ /spl Phi//sub 0//Hz/sup 1/2/ in the double stage configuration, measured at a temperature 4.2 K using direct read out electronics. In combination with an intermediary transformer, the current resolution of the SQUID is as low as 1.25 pA/Hz/sup 1/2/ with an input coil inductance of 100 nH.
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 superconducting quantum interferometer with two quantization loops, the so-called double SQUID, or D-SQUID, is a modification of the well-known rf SQUID. The modification consists of a replacement of the one junction of the rf SQUID by a superconducting loop with two Josephson junctions. This device can be used to transform the weak magnetic flux applied to the loop with junctions to a voltage across the tank circuit inductively coupled to the other loop. As has previously been shown in experiments [G. S. Krivoy and H. Koch, J. Appl. Phys. 74, 2925 (1993)], D-SQUIDs have an extremely large output signal swing up to 1 mV and a transfer function of several mV/(h/2e). In this paper, a D-SQUID theory using a numerical and an analytical approach is developed. The theoretical results are compared with the above-mentioned experiments.
We performed an in-depth numerical analysis of high-inductance bi-SQUIDs with normalized inductance of its one junction loop l ≫ 1. This is desired for better coupling with the external signals and for the high-temperature superconductor implementations. Typically the high linearity (up to 90 dB) can be achieved in bi-SQUIDs at l ≫ 1 at which its flux-to-voltage characteristic has a distinct triangular shape. We showed that the high linearity can be also achieved at l > 1, when the bi-SQUID has a hysteretic response. The critical current of the third Josephson junction is to be of the same order as the one of the other two Josephson junctions, and the inductance lDC of the second (two junction) loop is allowed to be as high as about one-fourth in the presence of the high linearity.
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.