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

TL;DR

This paper provides a quantum mechanical analysis of superconducting travelling-wave parametric amplifiers, exploring their noise, gain, and squeezing properties, and revealing fundamental limits and effects of impedance mismatch and thermal noise.

Contribution

It introduces a comprehensive quantum analysis of TWPAs, including effects of impedance mismatch, idler modes, noise, and squeezing, advancing understanding of their quantum-limited performance.

Findings

TWPAs are quantum-limited amplifiers with minimum added noise of half a quantum.

Impedance mismatch restricts pump amplitude and gain.

High gain doubles thermal noise due to wave-mixing.

Abstract

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