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Applied Physics Letters

Tunable narrow-linewidth oscillations and current-voltage characteristics of a resistive dc SQUID

J. M. V. Verschueren, A. A. Uiterwaal, Rob W. van der Heijden, P. Wyder

Published Jul 15, 1983• 12 citations
Publisher

Abstract

The output voltage of a dc superconducting quantum interference device (SQUID) containing a resistive section Rs oscillates at a frequency νq =Vs/ φ0 (φ0=flux quantum) when a current controlled voltage Vs is maintained across Rs. These oscillations have been observed from ∼10−1 to 1011 Hz, using Rs values ranging from ∼10−10 to ∼10−3 Ω in low inductance (∼10−10 H) point contact SQUID loops. At high frequencies, they manifest themselves in the dc current-voltage characteristics by inducing extra current steps.

DOI
10.1063/1.94258

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The output voltage of a dc superconducting quantum interference device (SQUID) containing a resistive section Rs oscillates at a frequency νq =Vs/ φ0 (φ0=flux quantum) when a current controlled voltage Vs is maintained across Rs. These oscillations have been observed from ∼10−1 to 1011 Hz, using Rs values ranging from ∼10−10 to ∼10−3 Ω in low inductance (∼10−10 H) point contact SQUID loops. At high frequencies, they manifest themselves in the dc current-voltage characteristics by inducing extra current steps.
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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.
Resistive two-junction SQUIDs (RSQUIDs) made from high-temperature superconductors are being developed as narrow-linewidth tunable oscillators in the GHz frequency range. We present here the results of numerical simulation of RSQUIDs of this type. These studies have identified conditions where sub-harmonic steps and other features are apparent in the current-voltage characteristics, driven by the internally-generated heterodyne frequency. The behavior is sensitive to the frequency (set by the voltage across the resistive element in the RSQUID), the temperature and also the loop inductance. We have studied the effects of thermal noise on these features. We also assess how these effects might be observed, and consider how they might affect practical applications of high frequency heterodyne RSQUID oscillators.
The electrical equations of a resonant circuit fed with a radio-frequency current and inductively coupled to a weakly superconducting loop have been derived. The current-voltage characteristic of the rf superconducting quantum interference device can then be calculated and studied as a function of the junction resistance or of the resonance frequency, enabling its behavior to be better understood. As shown by Kurkijärvi, the large positive slope of the steps and the rounding of the characteristic result from thermal noise. However, in order to explain quantitatively the experimental results concerning, namely, point contact weak links which are generally oxidized or which have several contact points, it is useful to remark that the connection between the two superconductors constituting the Josephson junction may be made from n resistive paths. The mean thermal energy of the fluctuating flux is then close to nkbT instead of kbT if the inductances linking the contact points are large enough, that is, on the order of 10−11 H.
We have developed a radio frequency bias current scheme with reversal frequency up to 50 MHz for dc superconducting quantum interference devices (SQUIDs). The SQUID and the readout electronics, were connected via a quarter wavelength (/spl lambda//4) transmission line. This transmission line not only transported the SQUID signal, but also served as the resonant matching circuit. For a dc SQUID of inductance 115 pH (loop size 75/spl times/75 /spl mu/m/sup 2/), we measured a flux noise of 33 /spl mu//spl phi//sub 0///spl radic/Hz at 77 K in the flux locked loop configuration. The corner frequency of 1/f noise was less than 0.5 Hz.
At an extremely low temperature of 20 mK, we measured the loop current in a tunable rf superconducting quantum interference device (SQUID) with a dc-SQUID. By adjusting the magnetic flux applied to the rf-SQUID loop (Φ f ) and the small dc-SQUID (Φ cjj f ), respectively, the potential shape of the system can be fully controlled in situ. Variation in the transition step and overlap size in the switching current with a barrier flux bias are analyzed, from which we can obtain some relevant device parameters and build a model to explain the experimental phenomenon.