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

Abstract

The underlying nonlinear mechanisms behind the operation of travelling-wave parametric amplifiers (TWPAs) are important in determining their performance in terms of added noise, maximum gain, and bandwidth. We describe a method of characterising the underlying nonlinearity of a superconducting material in terms of its dissipative-reactive ratio and the response time of the underlying microscopic processes. We describe and calculate the different behaviour arising from the equilibrium supercurrent nonlinearity, which has low dissipation and fast response time, and the non-equilibrium heating nonlinearity, which has high dissipation and slow response time. We have fabricated TWPAs based on Al and Ti, and characterised their nonlinearities using our analysis. For both Al and Ti, the measured dissipative-reactive ratios and response times are quantitatively similar to predictions for the non-equilibrium heating nonlinearity. In line with this, we were able to obtain more than 20 dB of peak power gain, although only over a narrow bandwidth of a few kilohertz.

Effects of reactive, dissipative and rate-limited nonlinearity on the behaviour of superconducting parametric amplifiers

“…Notice, however, that the amplifier gain always dips below the black dotted line to the right of the band edge above the pump frequency. This phenomena is characteristic of amplification via a rate-limited nonlinearity and has been discussed in detail by Zhao [21].…”

“…We have used δ here to distinguish these changes in f 0 and Q i , measured relative to the operating point values, from those in (7), which are measured relative to the zero readout power values. (65) shows we may identify q as the rate of change of the complex pole of the resonator with respect to fractional changes in the stored energy, as measured at the operating point, while maintaining the steady state condition (21). This definition will prove useful for the experimental measurement of q.…”