  We report on the observation of a novel manifestation of saturation-induced
optical bistability in a resonantly pumped optical ring cavity interacting
strongly with a cloud of atoms via a narrow atomic transition. The bistability
emerges, above a critical pump rate, as an additional peak in the cavity's
normal mode spectrum close to atomic resonance. This third transmission peak is
usually suppressed due to strong resonant absorption, but in our experiment it
is visible because of the linewidth of the atomic transition being much smaller
than that of the cavity, which sets the experiment into the bad-cavity regime.
Relying on complete saturation of the transition, this bistability has a
quantum origin and cannot be mimicked by a classical material presenting a
nonlinear refraction index. The appearance of the central peak in addition to
the normal modes is predicted by a semi-classical model derived from the
Tavis-Cummings Hamiltonian from which we derive a bistability phase diagram
that connects our observations with former work on optical bistability in the
good cavity regime. The phase diagram reveals several so far unexplored
bistable phases.
