Three-wave mixing in travelling-wave parametric amplifiers*

We develop a theory for a Josephson junction based travelling-wave parametric amplifier (TWPA) operating in the three-wave mixing regime and propose a scheme for achieving a high gain [1]. We take into account the discreteness of the Josephson junction chain to fully characterise a negative effect of spectral dispersion at high frequencies close to the cutoff. We also analyse the gain suppression by the high harmonic generation at the small frequency part of the spectrum. To achieve a high gain, we propose to engineer a chain with a spectral gap and to place the pump frequency above the gap close to the spectral cutoff. We find that there exists a sweet spot for the pump, where the signal injected below the gap and the pump are phase matched, while up-conversion is inhibited. Under these conditions an efficient amplification, above 20 dB, occurs within a bandwidth in the GHz range.

[1] H. Renberg Nilsson, A. Fadavi Roudsari, D. Shiri, P. Delsing, and V. Shumeiko, A high gain travelling-wave parametric amplifier based on three-wave mixing, 2022. doi:

10.48550/ARXIV.2205.07758. [Online]. Available: https://arxiv.org/abs/2205.07758.