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Optical lattice clock systems with ultra-cold strontium-88 atoms have beenused to demonstrate superradiant lasing and magnetic field-controlled opticaltransmission. We explain these phenomena theoretically with a rigorous modelfor three-level atoms coupled to a single cavity mode. We identify a class ofdark atom-light dressed states which become accessible due to mixing withbright dressed states in the presence of a magnetic field. We predict thatthese states, under moderate incoherent pumping, lead to lasing with alinewidth of only tens of Hz, orders of magnitude smaller than the cavitylinewidth and the atomic incoherent decay and pumping rates.

Magnetic Field-controlled Transmission and Ultra-narrow Superradiant Lasing by Dark Atom-light Dressed States