Quantum noise in heterodyne detection

A fully quantum mechanical theory of diode mixers which includes quantization of the external circuit is presented. We find that Tucker's theory for SIS mixer conversion efficiencies is correct, but that his expression for the measurement noise must be augmented by an amount corresponding to half a photon at every frequency to which the mixer responds. Noise in high quality SIS mixers is shown to be accurately described by the conceptually simpler photodiode mixer noise theory. The radiation coupling efficiency term, η, which appears in photodiode theory turns out to be the coupling efficiency between the signal source admittance and the admittance which the SIS presents to the LO. Our theory reduces to Caves' quantum linear amplifier formalism, and therefore predicts measurement noises bounded by the quantum lower limit of
hv/k_{B}
. Predictions of performance versus frequency for SIS's are made. We predict that NbN SIS's will behave as nearly ideal photodiodes for frequencies as high as 3000 GHz.