Semiclassical theory of the photon echo: Application to polar fluids

The photon echo experiment probes the dynamical processes that cause the decay of a coherent macroscopic electric polarization. Application of the technique to liquid solutions permits the study of the molecular motions that are strongly coupled to an electronic transition. We develop a semiclassical approximation to the photon echo observable, based on the use of Wigner equivalents of quantum operators, that we demonstrate to be accurate for all values of the delay time between the two pulses of the photon echo. In this approximation, the echo arises from fluctuations in the spectroscopic transition frequency, as the fluid evolves on a potential surface that is the arithmetic mean of the ground and excited state surfaces. The echo may then be calculated from nonequilibrium molecular dynamics simulations. We use this method to calculate the photon echo for a fluid of dipolar soft spheres. The results are compared to calculations of the absorption spectrum for this model, and to previous calculations of the effects of solvent dynamics on optical spectroscopic observables.