  We report coherent frequency conversion in the gigahertz range via three-wave
mixing on a single artificial atom in open space. All frequencies involved are
in vicinity of transition frequencies of the three-level atom. A cyclic
configuration of levels is therefore essential, which we have realised with an
artificial atom based on the flux qubit geometry. The atom is continuously
driven at two transition frequencies and we directly measure the coherent
emission at the sum or difference frequency. Our approach enables coherent
conversion of the incoming fields into the coherent emission at a designed
frequency in prospective devices of quantum electronics.
