Frequency dependence of quasiparticle mixers

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Abstract
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.