Quantum theory of line shapes in coherent Raman spectroscopy of gases and liquids

The fully quantum mechanical theory of coherent Raman scattering in gases and liquids is developed. In this theory, the electromagnetic radiation is described as a quantized field, and the quantum mechanical transition amplitude for the scattering process is calculated. This is formally different from the usual semiclassical theory in which the radiation field is characterized as a classical electromagnetic wave and nonlinear susceptibilities are used to describe the interaction of radiation and matter. The Doppler broadened line shape for the ideal gas is calculated and found to be non-Gaussian with a width that is 1.2 times larger than the Doppler width for spontaneous Raman scattering in the forward direction. This differs from a previously published result. The rotational-vibrational band shape is shown to be related to a correlation function for rotational-vibrational motion. This correlation function is the same as that describing spontaneous Raman scattering, but the relationship of the correlation function to the spectrum is different. In the absence of correlations between rotation and vibration the spectrum can be related to a Laplace transform (with an imaginary argument) of a rotational correlation function. The line shape is calculated for two special cases, free rotational motion and Brownian rotational motion.