Low-noise cryogenic microwave amplifier characterization with a calibrated noise source

Parametric amplifiers have become a workhorse in superconducting quantum computing, however research and development of these devices has been hampered by inconsistent, and sometimes misleading noise performance characterization methodologies. The concepts behind noise characterization are deceptively simple, and there are many places where one can make mistakes, either in measurement or interpretation and analysis. In this article we cover the basics of noise performance characterization, and the special problems it presents in parametric amplifiers with limited power handling capability. We illustrate the issues with three specific examples: a high-electron mobility transistor amplifier, a Josephson traveling-wave parametric amplifier, and a Josephson parametric amplifier. We emphasize the use of a 50-$\Omega$ shot noise tunnel junction (SNTJ) as a broadband noise source, demonstrating its utility for cryogenic amplifier amplifications. These practical examples highlight the role of loss as well as the additional parametric amplifier `idler' input mode.