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Applied Superconductivity

Modeling the performance of high temperature superconductor based sin and sis quasiparticle mixers

K. Koupnetsov, L. Coffep, John pasadpinski

Published Oct 1, 1994• 3 citations
Publisher
DOI
10.1016/0964-1807(94)90074-4

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An analysis of the frequency dependence of superconductor-insulator-normal (SIN) and superconductor-insulator-superconductor (SIS) quasiparticle mixers is presented. Power-law expressions for conversion loss and mixer shot-noise temperature for the double-sideband SIN mixer are derived from the Tucker theory for the case of a source conductance which is small compared to the conductance of the junction. For an ideal SIN tunnel junction at T=0 the mixer conversion efficiency is shown to decrease approximately linearly with frequency up to f=Δ/h. From f=Δ/h to 2Δ/h the conversion efficiency remains approximately constant, while above f=2Δ/h it rolls off as the inverse square of the frequency. Expressions for the shot-noise contribution to the mixer noise temperature are also derived. At frequencies up to f=Δ/h the noise temperature rises as the square root of the frequency. From f=Δ/h to f=2Δ/h the noise temperature of the mixer increases linearly with frequency, whereas above f=2Δ/h it rises as the cube of the frequency. Conversion efficiency and noise temperature are also calculated numerically for the SIN mixer. Good agreement is found between the frequency dependencies calculated analytically in the limit of small local oscillator power and the numerical calculations for optimal pumping. The frequency dependence of the nonideal SIS junction is also analyzed, and shown to yield similar results, with the characteristic frequencies Δ/h and 2Δ/h for a SIN mixer transformed into 2Δ/h and 4Δ/h, respectively. Expressions also are derived for the saturation power as a function of frequency.

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An analysis of the frequency dependence of superconductor-insulator-normal (SIN) and superconductor-insulator-superconductor (SIS) quasiparticle mixers is presented. Power-law expressions for conversion loss and mixer shot-noise temperature for the double-sideband SIN mixer are derived from the Tucker theory for the case of a source conductance which is small compared to the conductance of the junction. For an ideal SIN tunnel junction at T=0 the mixer conversion efficiency is shown to decrease approximately linearly with frequency up to f=Δ/h. From f=Δ/h to 2Δ/h the conversion efficiency remains approximately constant, while above f=2Δ/h it rolls off as the inverse square of the frequency. Expressions for the shot-noise contribution to the mixer noise temperature are also derived. At frequencies up to f=Δ/h the noise temperature rises as the square root of the frequency. From f=Δ/h to f=2Δ/h the noise temperature of the mixer increases linearly with frequency, whereas above f=2Δ/h it rises as the cube of the frequency. Conversion efficiency and noise temperature are also calculated numerically for the SIN mixer. Good agreement is found between the frequency dependencies calculated analytically in the limit of small local oscillator power and the numerical calculations for optimal pumping. The frequency dependence of the nonideal SIS junction is also analyzed, and shown to yield similar results, with the characteristic frequencies Δ/h and 2Δ/h for a SIN mixer transformed into 2Δ/h and 4Δ/h, respectively. Expressions also are derived for the saturation power as a function of frequency.
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.
Heterodyne mixers for millimeter wavelengths which have conversion gain and noise comparable to the quantum limit can be made using the non-linearity of the quasi-particle I-V curve of SIS or SIN tunnel junctions. When the voltage range of the non-linearity becomes small compared with hω/e, classical device theory breaks down and photon assisted tunneling theory must be used to understand mixer performance. In this paper we describe detailed computer simulations of SIS and SIN quasiparticle mixers. Predictions for conversion efficiency and noise are given for both devices as a function of operating frequency, bias voltage, RF source conductance and local oscillator power. A novel type of SIN harmonic mixer is proposed for which gain is also predicted.