Reflection-enhanced gain in traveling-wave parametric amplifiers

TL;DR

This paper develops an analytical model for traveling-wave parametric amplifiers that incorporates reflections, revealing that reflections enhance gain and suppress nonlinear phase modulations, with experimental validation on superconducting devices.

Contribution

The paper introduces an analytical solution for TWPA gain that accounts for reflected waves, extending standard coupled mode theory to unmatched devices.

Findings

Reflections lead to gain enhancement in TWPA.

Reflections suppress nonlinear phase modulations.

Experimental results confirm theoretical predictions.

Abstract

The operating principle of traveling-wave parametric amplifiers is typically understood in terms of the standard coupled mode theory, which describes the evolution of forward propagating waves without any reflections, i.e. for perfect impedance matching. However, in practice, superconducting microwave amplifiers are unmatched nonlinear finite-length devices, where the reflecting waves undergo complex parametric processes, not described by the standard coupled mode theory. Here, we present an analytical solution for the TWPA gain, which includes the interaction of reflected waves. These reflections result in corrections to the well-known results of the standard coupled mode theory, which are obtained for both 3-wave and 4-wave mixing processes. Due to these reflections, gain is enhanced and unwanted nonlinear phase modulations are suppressed. Predictions of the model are experimentally demonstrated on two types of unmatched TWPA, based on coplanar waveguides with a central wire consisting of i) a high kinetic inductance superconductor, and ii) an array of 2000 Josephson junctions.