  We experimentally demonstrate the resonance fluorescence of a two-level
artificial atom strongly coupled to a single-mode cavity field. The effect was
theoretically predicted thirty years ago by Savage [Phys. Rev. Lett. 63, 1376
(1989)]. The system consists of a superconducting qubit circuit and a
one-dimensional transmission line resonator. In addition, a one-dimensional
transmission line strongly coupled to the atom serves as an open space. The
effect takes place, when a microwave field is applied to the cavity, which in
turn is resonantly coupled to the atom. The fluorescence spectrum is measured
via the emission into the transmission line. We find that the central peak is
determined by the atom spontaneous emission to the open space and the widths of
side peaks are largely determined by the coherent interaction between the atom
and the cavity, that is, the fluorescence spectrum here is very different from
that of the Mollow triplet. We also derive analytical form for the spectrum.
Our experimental results agree well with theoretical calculations.
