Symmetries in the optical Bloch equations and multiphoton processes

The optical Bloch equations exhibit symmetries that ale directly related to the probabilities of the processes of absorption and stimulated emission. As a matter of fact, a picture similar to that holding for a two-level system can be recovered also in multilevel systems and, in particular, for any multiphoton process tuned between a given couple of levels. Thus, new quantities, such as the generalized Einstein B coefficients, directly related to the probabilities of the involved process, and atomic level indicators, whose inversion signals the existence of gain for that given process, can be defined. It is shown how these lead to valuable conceptual simplifications and to the disclosure of new insights into some popular problems of quantum optics. In particular, the issue of an efficient gain process to be realized within a multilevel atom-field configuration, a problem closely related to the widely investigated problem of lasing configurations without population inversion, can be viewed entirely as a rate problem and therefore analyzed with increased confidence.