  We study a double quantum dot system coherently coupled to an electromagnetic
resonator. A current through the dot system can create a population inversion
in the dot levels and, within a narrow resonance window, a lasing state in the
resonator. The lasing state correlates with the transport properties. On one
hand, this allows probing the lasing state via a current measurement. On the
other hand, the resulting narrow current peak allows resolving small
differences in the dot properties, e.g., a small difference in the Zeeman
splittings of the two dots. For realistic situations relaxation processes have
pronounced consequences. Remarkably, they may even enhance the resolution
between different spin states by releasing a trapped population in the
off-resonant spin channel.
