Microwave Engineering of Parametric Interactions in Superconducting Circuits

Parametric interactions are the basis for critical and emerging superconducting quantum technologies such as quantum limited amplifiers and parametric circulators. For these devices to be practical in the context of frequency multiplexed, multi-qubit readout, they must be designed to have predictable performance over a relatively wide bandwidth. To that end, we developed a description of parametric interactions–frequency conversion and amplification processes–from a microwave engineering point of view, which allows us to harness established band-pass network-synthesis methods in our circuit designs. We will review our design methodology and its relation to the usual coupled-modes approach, then present data from two classes of parametrically-pumped Josephson devices that we designed accordingly. First, a matched parametric amplifier having 500 MHz instantaneous bandwidth with 20 dB flat gain based on a 3-pole Chebyshev network, and second, a Josephson circulator with 200 MHz bandwidth and 15 dB of isolation, built with hybrid passive and parametric coupling elements with a 2-pole matching network.