We investigate superradiance of an ensemble of atoms coupled to an integrated
superconducting LC-circuit. Particular attention is paid to the effect of
inhomogeneous coupling constants. Combining perturbation theory in the
inhomogeneity and numerical simulations we show that inhomogeneous coupling
constants can significantly affect the superradiant relaxation process.
Incomplete relaxation terminating in "dark states" can occur, from which the
only escape is through individual spontaneous emission on a much longer time
scale. The relaxation dynamics can be significantly accelerated or retarded,
depending on the distribution of the coupling constants. On the technical side,
we also generalize the previously known propagator of superradiance for
identical couplings in the completely symmetric sector to the full
exponentially large Hilbert space.
