Photon Statistics and Spectrum of Transmitted Light in Optical Bistability

A quantum description of the transmitted field is given. In the bistable situation, the stationary Glauber quasi probability distribution has two peaks thereby producing a first-order phase transition. For small incident field the linewidth of the transmitted light is proportional to the atomic density and becomes very narrow as the field approaches some critical value from below. Crossing this value the spectrum splits discontinuously into a triplet (dynamical Stark shift) where the central peak is as high as twice the side-bands.