Time correlations and squeezing phenomena in lasers

The conventional way of studying laser noise assumes analytic solution of the quantum problem for the laser field coupled to the active medium. A number of the laser schemes have been discussed, and predictions for noise reduction and for the squeezed state of field have been made. On the basis of first principles of the quantum mechanics, the conventional approach exhibits the relatively rare situation in which the quantum equations admit compact analytic solution. At the same time, the difficulty in interpreting the results seems to be unresolved. Specifically, it is very difficult to determine the relative contribution of each physical source of noise to the final fluctuation result. In this paper we attempt to shed more light on the important issue of interpreting and identifying the various fluctuation mechanisms in the laser. Specific in our consideration is that in interpreting the results we attempt not to lose the original rigor of the quantum set of equations. We generally believe that the basic sources (mechanisms) of noise in laser are (a) distribution of laser parameters (inhomogeneous broadening), (b) noise of the pump and relaxation in the medium (homogeneous broadening), and (c) pure quantum fluctuations (vacuum noise). Generally speaking, the problem is to identify each of them. Ralph and Savage introduced a stochastic time and developed a simple statistical model for multilevel laser schemes that relates fluctuations of the photon number to the fluctuations of time. We extend their approach into entire fluctuation domain so as to include quantum noise and make the theory as rigorous as the conventional quantum approach is supposed to be. Following the idea of Ralph and Savage, we introduce a random recycling time, which is defined as the time needed for an atom to be recycled from the lower lasing level to the upper one upon emitting a photon into the field. However, we define the recycling time as a quantum variable in terms of the density matrix for the dressed-atom states. A crucial point is that the meaning of the recycling time is sensitive to the definition of the excited state. Here a question arises as to the role of the relaxation effect in the dressed-atom picture. It is essential to modify the conventional dressed-atom picture to include correctly the relaxation effect. Macroscopic characteristics of the radiation field are exploited in order to take this relaxation effect into account. Detailed results are presented.