Dissipationless nonlinearity in quantum material Josephson diodes

Dissipationless nonlinearities for three-wave mixing are a key component of many superconducting quantum devices, such as amplifiers and bosonic qubits. So far, such third-order nonlinearities have been primarily achieved with circuits of concatenated Josephson tunnel junctions. In this work, we theoretically develop an alternative approach to realize third-order nonlinearities from gate-tunable and intrinsically symmetry-broken quantum material Josephson junctions. We illustrate this approach on two examples, an Andreev interferometer and a magnetic Josephson junction. Our results show that both setups enable Kerr-free three-wave mixing for a broad range of frequencies, an attribute that is highly desirable for amplifier applications. Moreover, we also find that the magnetic junction constitutes a paradigmatic example for three-wave mixing in a minimal single-junction device without the need for any external biases. We hope that our work will guide the search of dissipationless nonlinearities in quantum material superconducting devices and inspire other ways of characterizing symmetry breaking in quantum materials with microwave techniques.