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The underlying nonlinear mechanisms behind the operation of travelling-waveparametric amplifiers (TWPAs) are important in determining their performance interms of added noise, maximum gain, and bandwidth. We describe a method ofcharacterising the underlying nonlinearity of a superconducting material interms of its dissipative-reactive ratio and the response time of the underlyingmicroscopic processes. We describe and calculate the different behaviourarising from the equilibrium supercurrent nonlinearity, which has lowdissipation and fast response time, and the non-equilibrium heatingnonlinearity, which has high dissipation and slow response time. We havefabricated TWPAs based on Al and Ti, and characterised their nonlinearitiesusing our analysis. For both Al and Ti, the measured dissipative-reactiveratios and response times are quantitatively similar to predictions for thenon-equilibrium heating nonlinearity. We were able to obtain more than 20 dB ofpeak power gain, although only over a narrow bandwidth of a few kilohertz. Ourmethod of characterising the underlying nonlinearities could also be useful inthe understanding and design of other superconducting nonlinear devices such asparametric up-converters, kinetic inductance Fourier transform spectrometers,and resonator parametric amplifiers.

Nonlinear mechanisms in Al and Ti superconducting travelling-wave parametric amplifiers