Berry curvature dipole circuit quantum electrodynamics

Quantum three-wave mixing is an important resource in superconducting quantum circuits. The traditional implementation uses Josephson junction arrays and is activated by magnetic flux. Here we introduce the Berry curvature dipole (BCD) quantum circuit element, which achieves quantum three-wave mixing without breaking time-reversal symmetry. This quantum three-wave mixing results from the BCD nonlinear Hall effect in noncentrosymmetric quantum materials taken to a dissipationless, quantum coherent few-photon regime. We show how nonlinear Hall materials can be integrated to superconducting microwave circuits to accomplish multiphoton vacuum Rabi splittings and dynamical stabilization of bosonic Schrödinger cat states. Such BCD circuit quantum electrodynamics are a concrete exemplar of a physical resource for quantum information processing enabled by nonlinear response in quantum materials.