  Recently, a lasing effect has been observed in a superconducting nano-circuit
where a Cooper pair box, acting as an artificial three-level atom, was coupled
to a resonator. Motivated by this experiment, we analyze the quantum dynamics
of a three-level atom coupled to a quantum-mechanical resonator in the presence
of a driving on the cavity within the framework of the Lindblad master
equation. As a result, we have access to the dynamics of the atomic level
populations and the photon number in the cavity as well as to the output
spectrum. The results of our quantum approach agree with the experimental
findings. The presence of a fluctuator in the circuit is also analyzed.
Finally, we compare our results with those obtained within a semiclassical
approximation.
