Intensity dependence of the polarization tensor in a quantum treatment

Recently one of the authors published a paper concerning the exact quantum mechanical description of pressure-induced four-wave mixing in which the exact expression of the transition probability was found.1 In this approach, a formal solution for the problem of multifield interacting with a single multilevel atom is presented by treating the fields fully quantized and the states in a dressed atomic picture. If we think of the four-wave mixing experiments as a case where the ω a , ω b , and ω c waves are sent into the medium with the fourth wave at ω p generated by the mixing, the output amplitude should be proportional to the component of the polarization fluctuating at the frequency of ω p . Based on these results, we obtained an exact quantum mechanical expression for the polarization tensor. This paper intends to explore the photon number (intensity) dependence of the polarization tensor (susceptibility) and give a comparison of the line shapes for low and high intensity of the incoming three beams. Specifically, the corresponding terms for the 31st, 32nd and 33rd terms in the Bloembergen classical expression for the susceptibility tensor will be investigated in detail.2 For no dissipation we will plot and analyze the amplitude of the polarization component at ω p .