The ability to coherently couple arbitrary harmonic oscillators in a fully-controlled way is an important tool to process quantum information. Coupling between quantum harmonic oscillators has previously been demonstrated in several physical systems by use of a two-level system as a mediating element. Direct interaction at the quantum level has only recently been realized by use of resonant coupling between trapped ions. Here we implement a tunable direct coupling between the microwave harmonics of a superconducting resonator by use of parametric frequency conversion. We accomplish this by coupling the mode currents of two harmonics through a superconducting quantum interference device (SQUID) and modulating its flux at the difference (~ 7 GHz) of the harmonic frequencies. We deterministically prepare a single-photon Fock state and coherently manipulate it between multiple modes, effectively controlling it in a superposition of two different colours. This parametric interaction can be described as a beam-splitter-like operation that couples different frequency modes. As such, it could be used to implement linear optical quantum computing protocols on-chip.
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