SPECTRUM OF TRANSMITTED AND FLUORESCENT LIGHT IN ABSORPTIVE OPTICAL BISTABILITY

We consider a homogeneously broadened system of two-level atoms, driven by a coherent monochromatic field perfectly tuned to the atoms and to the cavity. On the basis of a suitable Fokker-Plank equation for the relevant (atomic and field) macroscopic variables, we calculate the fluctuations of the system around the stable steady states. These fluctuations in turn allow evaluating the line shape of the transmitted and fluorescent light. The incoherent parts of the two spectra show qualitatively the same behaviour. They are found to exhibit a hysteresis cycle with line narrowing at the boundaries of the cycle. For small incident field, the line width is proportional to the number of atoms. We consider both the case that the atomic line width is much smaller than the empty-cavity width and the opposite case. In the first situation, in which the dynamics is governed by the atoms, increasing the incident field intensity one finds the sudden appearance of a triplet with well-separated side bands (discontinuous dynamical Stark shift). In the second case, in which the dynamics is governed by the field, no dynamical Stark shift appears at all. A detailed comparison of the spectra of transmitted and fluorescent light is given. We calculate also the atom-atom correlations, which are found to be relevant only in the co-operative stationary state. All the results hold both for the purely radiative and for the collisional case. © 1979 Società Italiana di Fisica.