Modeling and simulation of Radiofrequency Quantum Upconverters*

The Radiofrequency Quantum Upconverter (RQU) coherently imprints a low frequency (<300 MHz) flux signal onto an output microwave (4-6 GHz) drive tone using a parametric interaction between a Josephson-junction interferometer and a superconducting microwave resonator, enabling quantum measurement of low frequency electromagnetic modes. The Josephson-junction interferometer consists of three junctions in two loops, which enables separation between low- and microwave-frequency currents at specific flux bias points. A three-junction interferometer can be used in particular bias conditions to isolate the microwave carrier from modes in the coupled low-frequency input to prevent decoherence. We model and simulate signal propagation through our device and show that for weak microwave drives the Josephson interferometer inductance is a function of applied external flux. We then consider nonlinear dynamics that occur in the presence of high drive powers or non-negligible interferometer geometric inductance. Finally, we describe backaction-evasion protocols that can be implemented with RQUs.