  We have realized a hybrid solid-state quantum device in which a
single-electron semiconductor double quantum dot is dipole coupled to a
superconducting microwave frequency transmission line resonator. The dipolar
interaction between the two entities manifests itself via dispersive and
dissipative effects observed as frequency shifts and linewidth broadenings of
the photonic mode respectively. A Jaynes-Cummings Hamiltonian master equation
calculation is used to model the combined system response and allows for
determining both the coherence properties of the double quantum dot and its
interdot tunnel coupling with high accuracy. The value and uncertainty of the
tunnel coupling extracted from the microwave read-out technique are compared to
a standard quantum point contact charge detection analysis. The two techniques
are found to be consistent with a superior precision for the microwave
experiment when tunneling rates approach the resonator eigenfrequency.
Decoherence properties of the double dot are further investigated as a function
of the number of electrons inside the dots. They are found to be similar in the
single-electron and many-electron regimes suggesting that the density of the
confinement energy spectrum plays a minor role in the decoherence rate of the
system under investigation.
