Quantum analysis of second-order effects in superconducting travelling-wave parametric amplifiers

We have performed a quantum mechanical analysis of travelling-wave parametric amplifiers (TWPAs) in order to investigate five experimental phenomena related their operations, namely the effect impedance mismatch, presence upper idler modes, and thermal noise, generation squeezed states, preservation pre-squeezed states during amplification. Our uses momentum operators describe spatial evolution quantised modes along TWPA. calculate restriction placed on pump amplitude as well amplifier gain result mismatch between TWPA its external system. apply our demonstrate that they will suppressed gain. show an ideal is indeed quantum-limited - i.e. it introduces half-quantum zero-point fluctuation which minimum possible noise contribution for phase-preserving linear amplifier. analyse associated with by considering distributed sources transmission line. predicts doubling high limit wave-mixing signal modes. study operation DC bias current, shown highly can principle be generated. However, amplifying state using non-degenerate generally reduces squeezing advantage.