  We consider a system composed of a single artificial atom coupled to a cavity
mode. The artificial atom is biased such that the most dominant relaxation
process in the system takes the atom from its ground state to its excited
state, thus ensuring population inversion. A recent experimental manifestation
of this situation was achieved using a voltage-biased superconducting charge
qubit. Even under the condition of `inverted relaxation', lasing action can be
suppressed if the `relaxation' rate is larger than a certain threshold value.
Using simple transition-rate arguments and a semiclassical calculation, we
derive analytic expressions for the lasing suppression condition and the state
of the cavity in both the lasing and suppressed-lasing regimes. The results of
numerical calculations agree very well with the analytically derived results.
We start by analyzing a simplified two-level-atom model, and we then analyze a
three-level-atom model that should describe accurately the recently realized
superconducting artificial-atom laser.
