  We report on the on-chip detection of microwaves in the frequency range
around 100GHz. For the purpose of detection, we employ a discrete transport
channel triggered in a superconducting single-electron transistor by
photon-assisted tunneling of quasiparticles. The technique is successfully
applied to observe the spectrum of the dressed states of a model cQED system
consisting of a superconducting coplanar resonator coupled to a quantum
Josephson oscillator. The dressed states appear as typical resonance
anticrossing exhibiting, in our case, an expectedly wide frequency splitting
corresponding to the Jaynes-Cummings coupling strength, g/pi~10GHz. Due to the
high decay rate, gamma~20-40GHz, in the very transparent Josephson junctions
used, the strong coupling limit, g>>gamma, which is required for qubit
operation, is not achieved, and the photon population in the resonator is low,
<n>~1. Remarkably, the continuous readout of the low population states
demonstrates the high microwave sensitivity of the detector.
