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Revue de Physique Appliquée

Mixing in superconducting weak links : numerical calculations and experimental results

F. Auracher, T. Van Duzer

Published Jan 1, 1974• 23 citations
Publisher

Abstract

We report here numerical calculations on the properties of superconducting weak links as mixers with external local oscillators (LO). Our calculations are based on the resistively shunted-junction model. We assume that the LO and the signal are ideal current sources of amplitudes ILO and IS and of frequencies ωLO and ωs, respectively. We calculate the IF voltage across the weak link as a function of the bias current, the LO current amplitude ILO, and the normalized signal frequency Ωs = ħωs/(2 e Ic R), where Ic is the critical current and R is the shunt resistance. If ωIF/ωLO and Is/Ic are small, we find a linear IF response. Using this method we find the frequency dependence of the IF response, estimate the conversion efficiency for the matched case in both the absence and the presence of noise, and calculate the required LO power. We have fabricated thin-film constrictions by using electron lithography. We have made constrictions of indium films with thicknesses of ~ 1 200 A with widths as narrow as 2 000 A and lengths as short as 1 000 A and have studied their I-V characteristics in the presence of RF radiation and measured their X-band mixing properties. We have measured an NEP of 10-13 W/Hz1/2 and a dynamic range of 23 dB (3 dB deviation from linearity) and estimate that, with optimum matching, these would become 3 × 10-18 W/Hz1/2 and 74 dB, respectively.

DOI
10.1051/rphysap:0197400901023300

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Journal of Physics D Applied Physics•Sep 14, 1981•3 citations
We report here numerical calculations on the properties of superconducting weak links as mixers with external local oscillators (LO). Our calculations are based on the resistively shunted-junction model. We assume that the LO and the signal are ideal current sources of amplitudes ILO and IS and of frequencies ωLO and ωs, respectively. We calculate the IF voltage across the weak link as a function of the bias current, the LO current amplitude ILO, and the normalized signal frequency Ωs = ħωs/(2 e Ic R), where Ic is the critical current and R is the shunt resistance. If ωIF/ωLO and Is/Ic are small, we find a linear IF response. Using this method we find the frequency dependence of the IF response, estimate the conversion efficiency for the matched case in both the absence and the presence of noise, and calculate the required LO power. We have fabricated thin-film constrictions by using electron lithography. We have made constrictions of indium films with thicknesses of ~ 1 200 A with widths as narrow as 2 000 A and lengths as short as 1 000 A and have studied their I-V characteristics in the presence of RF radiation and measured their X-band mixing properties. We have measured an NEP of 10-13 W/Hz1/2 and a dynamic range of 23 dB (3 dB deviation from linearity) and estimate that, with optimum matching, these would become 3 × 10-18 W/Hz1/2 and 74 dB, respectively.
Using a superconducting weak link (bridge) made of YBCO, the authors have successfully observed Josephson harmonic mixing between a local oscillation (LO) at X band and a signal at Ka band. Specifically, fourth-order harmonic mixing between 35.47 GHz and 8.843 GHz was observed. For a given signal level, the IF (intermediate frequency) responses depended strongly on both LO level and DC voltage bias across the junction. For zero bias, there is still IF output which is characteristic of even-order harmonic mixing. When the LO power level is such that the zero voltage current is suppressed to the second zero, the IF responses are maximum if the junction is biased between the zeroth and first steps induced by the LO. Also studied is the internal oscillation-mixing. An incoming signal at either X or Ka band gives rise to IF signal peaks if the junction is biased at voltages such that the corresponding internal Josephson frequencies are equal to, or harmonics of, the incoming signal frequency.>
The goals of the work were to fabricate superconductive thin-film constrictions with an electron microscope and to test them as mixers. During the grant period indium and vanadium constrictions were made with submicron dimensions and these were tested in detection and mixing modes. Most of the tests were conducted at X-band frequencies and some were done at V-band. A computer program was developed to study the theoretical behavior of a circuit model of Josephson devices such as thin-film constrictions. Considerable information was derived from the calculations and good agreement with experiments was obtained in some cases. In the process of developing sufficient understanding of electron-resist exposures, the author worked out a theory which gives general guidance for the use of electron resists for microdevice fabrication. Simple arrays of two and three devices were studied under dc conditions. A theoretical description of a generally asymmetric array was developed, taking account of the self- and mutual inductances.
In this paper, we present our latest results on the properties of superconducting weak links prepared in Mo films by ion-implantation and in Nb films by electron-beam lithography. In the case of the ion-implanted weak links, which structurally resemble proximity-effect bridges, we find that the static properties are quite well described by a recent theory of Likharev and Yakobson. We further find that the rf response of these weak links is in excellent agreement with quasistatic resistively-shunted-junction model calculations based on a sinusoidal current-phase relation at those temperatures for which such a current-phase relation is predicted by the static theory of Likharev and Yakob-son. For the e-beam fabricated Nb bridges, which have the Dayem bridge geometry, our sample preparation techniques have allowed us to produce bridges and two-junction interferometers in which the link dimensions are as small as about 2000 Angstroms. We find that Josephson effects are observable in these bridges even when the bridge dimensions exceed the temperature-dependent coherence length by about an order of magnitude, but are still less than the effective thin-film penetration depth.
Microwave mixing and parametric conversion in YBa/sub 2/Cu/sub 3/O/sub 7/ microbridges were investigated. The devices have been operated as down-converters, converting a 20-GHz radio frequency to a 1.5-GHz intermediate frequency under the action of an 18.5-GHz local oscillator. The microbridges were fabricated both as granular films on MgO substrates possessing grain boundary weak links and as epitaxial films deposited over substrate steps in LaAlO/sub 3/ substrates. The authors have measured conversion gains as high as -8+or-4 dB when mixing on the nonlinear resistive (superconducting-normal) transition and as high as -30 to -40 dB when parametrically converting via the nonlinear inductance of the bridge at bias currents less than the critical current. Output referred noise powers as low as -206 dB/Hz (3*10/sup -21/ W/Hz) have been measured. In some samples, noise switching events were observed.>
We have investigated high-frequency limits of superconducting quasiparticle mixers from experiments on Al/Al-oxide-In/Al (or Ag) tunnel junctions, and from calculations based on Tucker’s quantum theory of mixing (QTM). The small superconducting energy gap of Al enabled us to study mixer performance at around the junction gap frequency, fg =(Δ1+Δ2)/h≊87 GHz, of superconductor-insulator-superconductor (SIS) mixers, and at twice the junction gap frequency for S-I-normal metal (SIN) mixers ( fg =Δ1/h) with available millimeter wave sources. Because of the low transition temperature of Al (Tc ≊1.3 K), a dilution refrigerator was used for providing temperatures below 1 K. The best mixer conversion efficiency was obtained for a low-resistance (∼34 Ω) six-junction array SIS mixer operated at f/fg ≊1 (in this case 73 GHz). The coupled single sideband conversion gain (with no image rejection) was −13.8 dB and the available conversion gain was estimated to −8.4 dB. Complicating nonequilibrium phenomena made it difficult to compare the performance of these relatively high-current-density mixers to the QTM. However, good agreement between calculated and corresponding measured conversion efficiencies and dynamic resistance values was obtained for the low-current-density mixers. Noise due to switching between rf-induced Josephson steps and interference from Josephson mixing could be quenched by a magnetic field. Several high-frequency limits are considered in this paper (such as Josephson switching noise, nonequilibrium phenomena, pair breaking, and energy gap limitations). Our results indicate that submillimeter wave SIS mixer receivers are likely to perform well, at least up to their gap frequencies, i.e., the THz region for large gap superconductors. Our QTM calculations showed that conversion gain larger than unity should be possible up to twice the gap frequency. Above this frequency the conversion loss will increase rapidly.
Measurements at 3 GHz of the microwave properties of a superconducting thin-film microbridge coupled to a narrowly tuned strip-line resonator (coupled Q approximately 10 3 ) indicate that such a device displays the same variations in small-signal impedance as predicted by the resistively shunted junction model of a Josephson weak-link. Whenever this impedance becomes negative the microbridge is found to generate microwave radiation whose frequency is determined not by the junction bias voltage but by the natural resonance of the strip-line.