  Optical lattice clock systems with ultra-cold strontium-88 atoms have been
used to demonstrate superradiant lasing and magnetic field-controlled optical
transmission. We explain these phenomena theoretically with a rigorous model
for three-level atoms coupled to a single cavity mode. We identify a class of
dark atom-light dressed states which become accessible due to mixing with
bright dressed states in the presence of a magnetic field. We predict that
these states, under moderate incoherent pumping, lead to lasing with a
linewidth of only tens of Hz, orders of magnitude smaller than the cavity
linewidth and the atomic incoherent decay and pumping rates.
