Date of Award

Fall 10-1-2021

Document Type


Degree Name

Doctor of Philosophy (PhD)


Applied Physics

First Advisor

Devoret, Michel


Three-wave mixing, by which a photon splits into two correlated photons and vice versa, is a powerful quantum process with many applications in fundamental quantum mechanics experiments and quantum information processing. However, in superconducting circuits, the predominant form of nonlinearity provided by a Josephson junction is only of even order, and thus symmetry forbids three-wave mixing. This Kerr nonlinearity is useful in its own right for engineering quantum operations, but it is accompanied by unavoidable frequency shifts that become especially problematic as the number of interacting electromagnetic modes, and therefore frequency crowding, increases. How then can we endow superconducting devices with the necessary nonlinearity to perform three-wave mixing? In this thesis, we introduce a simple and compact way to add three-wave-mixing capabilities to a superconducting circuit: the superconducting nonlinear inductive element (SNAIL). Additionally, we optimize these devices for quantum-coherent three-wave mixing applications. The many orders of magnitude over which circuit nonlinearities may be designed allow a rich space for different behaviors. We focus on three-wave mixing for single-mode squeezing in two distinct contexts: quantum-noise-limited parametric amplification, and protection of quantum information in a Schrödinger cat qubit. The former showcases the capability to design three-wave-mixing processes free of residual Kerr nonlinearity; the latter explicitly includes Kerr nonlinearity to protect quantum information from decoherence and quickly manipulate it. Both applications indicate the importance of three-wave mixing in quantum information contexts and for the exploration of fundamental quantum effects.