Some difficulties of recently proposed experimental arrangements for the demonstration of antibunching based on non-linear optical processes are discussed. New proposals are given on the basis of non-degenerate sum-frequency and second harmonic generation in an optical resonator.
The difference in the group velocities for the signal and the idler wave, interacting with a sum-frequency wave in a non-linear crystal, is shown to provide a memory mechanism which determines the length of the mode volume occurring in the usual single-mode description of this process in connection with photon antibunching. The consideration also includes the degenerate case (second harmonic generation). The results suggest the use of a c.w. picosecond laser as a primary light source in an experiment designed to demonstrate the antibunching effect. The basic set-up of such an experiment is described.
We have formulated expressions providing the number of terms (Y-G diagrams)1contributing to an n-th order susceptibility of a non-linear optical process. Obtaining an accurate count of these terms is important for diverse reasons: a) To accurately specify the number of terms needed to evaluate the nonlinear optical susceptibility either analytically or numerically, b) To help develop sequences of diagrammatic contributions which can be summed to provide analytical results for the strong interaction limit. An example is the two-level system for semiclassical and quantized fields, c) To treat two or more processes (terms) which could give rise to interference, resulting, for example, in extra resonances due to a lack of complete coherence, d) To generalize results from quantum electrodynamics to situations for which multiple photon interactions and zero point fluctuations associated with non-vacuum states need to be considered. We shall discuss the number of possible diagrams in terms of three factors, which we call a permutation factor relating to the number of possible frequencies that can be assigned to each interaction vertex, a commutation factor relating to interaction vertex assignment on the two sides of the diagram, and a state factor relating to the number of diagrams generated from an enumeration of specific material state assignments between interaction vertices. We will discuss the application of these results to several situations of interest including second harmonic generation, degenerate four-wave mixing, and resonant CARS (coherent anti-Stokes Raman scattering) in a four-level system. The relevance of the present results to experimental results which have been obtained will be discussed along with future directions which need to be addressed including the summability of diagrams under specific approximations, the calculation of expectation values, and the nonperturbative representation of processes.