A classical theory of pump–probe photodissociation for arbitrary pulse durations

The classical Condon picture for linear absorption spectroscopy is a time-honored approximation known to give accurate results for broad spectral lines. The generalization of the classical Condon picture to nonlinear spectroscopies, however, is a problem under current investigation. Bersohn and Zewail have proposed a phenomenological formula applicable to the pump–probe photodissociation of iodine cyanide (ICN). We undertake an investigation of classical approximations in pump–probe spectroscopy from first principles. We present a new classical formula for the probe absorption that is derived using the density matrix in phase space and is valid for arbitrary pulse durations. Conditions whereby the signal depends only on field spectral or temporal intensities are specified. The classical formula presented here is compared with exact quantum mechanical calculations of the probe absorption for a simple model of ICN. Our formula shows very good agreement with the quantum calculations. We recover the formula of Bersohn and Zewail in the case of pulses that are very short compared to the time scale of nuclear dynamics.