Tunable coupling between long-lived microwave cavity modes*

Superconducting microwave cavities are a promising resource for the storage of quantum states of photons. Further, coupling cavities to nonlinear transmon qubit modes enables the efficient manipulation and readout of these states. However, this results in increased relaxation and dephasing rates associated with the transmon. Thus, a direct coupling between neighboring cavities is a desirable resource for interfering quantum states stored in separate cavity modes. Here we discuss the implementation of an engineered coupling between two cavity modes via an RF-driven frequency-conversion that uses the nonlinearity of a transmon coupled to both cavities. Importantly, this coupling does not directly excite the transmon, thus suppressing the effect of transmon decoherence. We demonstrate the tunability of the coupling strength, which minimizes unwanted interactions, and realize a 50:50 beamsplitter two orders of magnitude faster than the cavity decoherence. We observe high-contrast interference between single microwave photons, which will be useful as an element in larger quantum algorithms.