Quantum optics nonlinear phenomena

The phase distribution function (143) allows for calculations of the phase variances for the individual modes as well as the phase correlations between the two modes by performing simple integrations over the phase variables Qa and 0/,. Detailed discussion of the phase properties of the fields can be found in Ref. 16, and we will not repeat it here. The material presented in this section has been chosen as to illustrate how quantum noise, which is an indispensable ingredient of quantum description of optical fields, can be incorporated into the theory of nonlinear optical phenomena, in particular the phenomenon of second-harmonic generation. 

The atomic coherence and interference phenomenon in the simple three-level system sueh as EIT can be extended to more eomplicated multi-level atomic systems. A variety of other phenomena and applications involving three or four-level EIT systems have been studied in reeent years. In particular, phase-dependent atomic coherence and interference has been explored [52-66]. These studies show that in multi-level atomic systems coupled by multiple laser fields, there are often various types of nonlinear optical transitions involving multiple laser fields and the quantum interference among these transition paths may exhibit complicated spectral and dynamic features that can be manipulated with the system parameters such as the laser field amplitudes and phases. Here we present two examples of such coherently coupled multi-level atomic systems in which the quantum interference is induced between two nonlinear transition paths and can be eontrolled by the relative phase of the laser fields. 

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