Artificial Transmission Line Synthesis Tailored for Traveling-Wave Parametric Processes

Artificial transmission lines built with lumped-element inductors and capacitors form the backbone of broadband, nearly quantum-limited traveling-wave parametric amplifiers (TWPAs). When tailoring these transmission lines for parametric processes, nonlinear elements are added, typically nonlinear inductances in superconducting circuits, and energy and momentum conservation between interacting tones must be enforced through careful design of the ATL dispersion relation. However, a unified theoretical framework describing achievable dispersion relations is lacking. Here, I develop such a framework, borrowing from periodic structure theory and passive network synthesis. These complementary approaches divide the design space: periodic loading synthesis employs spatial modulation of frequency-independent components, while filter synthesis employs frequency-dependent responses in spatially-uniform components. The framework reveals fundamental constraints and enables the discovery of novel TWPA architectures. In particular, I design a kinetic inductance TWPA with a novel phase-matching architecture, and a backward-pumped Josephson TWPA exploiting an ambidextrous i.e., right-left-handed transmission line.