An analytic investigation of the superconductor quasiparticle mixer in the low power limit

The properties of an SIS (Superconductor-insulator-superconductor) mixer using a slightly nonideal junction, with finite local oscillator (LO) power, are determined by analytic expansion of the equations of the quantum theory of mixing. The result is that the conversion gain using any reasonably good quality SIS junction is essentially equal to that using a perfect junction. Quite to the contrary, the minimum noise temperature is controlled by the leakage current of the junction: the increase in the minimum added-noise temperature over the quantum limit T_Q=hω/2k is given by δ T_Q=(hω/k) √I ₀I₂/I₁; this minimum requires that the LO voltage across the junction is V_LO =(64I₀/I₂) ^1/4 hω/e. (I_n is the current measured on the unpumped I-V curve of the junction at voltage V₀+nhω/e). Therefore, although an SIS mixer using an ideal junction can reach the quantum noise limit only in the limit of zero LO power, even the most nearly ideal junctions require a considerable LO for best sensitivity