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Physical Review A

Rate processes affected by ultrashort-pulse fields

Benjamin Fain, S. H. Lin, W. X. Wu

Published Jul 1, 1989• 21 citations
Publisher

Abstract

In the femtosecond pump-probe pulse experiments, the pump pulse with duration comparable to or shorter than a typical vibrational period creates a nonstationary wave pocket. In this paper, we use the density-matrix method to treat the dynamic behavior of the system (embedded in a heat bath) in the femtosecond pump-probe pulse experiment. The expression for the coherence of the system due to the pumping laser is derived, and the generalized master equations for the dynamical behavior of the system after the pumping pulse is over are also obtained. Some numerical calculations are performed for a two-level system to demonstrate the time-dependent behaviors of memory kernel, rate constant, and population.

DOI
10.1103/physreva.40.824

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Journal of the Optical Society of America B•Jan 1, 1987•0 citations
In the femtosecond pump-probe pulse experiments, the pump pulse with duration comparable to or shorter than a typical vibrational period creates a nonstationary wave pocket. In this paper, we use the density-matrix method to treat the dynamic behavior of the system (embedded in a heat bath) in the femtosecond pump-probe pulse experiment. The expression for the coherence of the system due to the pumping laser is derived, and the generalized master equations for the dynamical behavior of the system after the pumping pulse is over are also obtained. Some numerical calculations are performed for a two-level system to demonstrate the time-dependent behaviors of memory kernel, rate constant, and population.
In femtosecond laser-pulse experiments the pump pulse, with duration comparable or shorter than a typical period of intra- or intermolecular vibrations, creates a nonstationary wave packet. In this paper we use the density-matrix method to analyze creation of space–time coherences by the pump pulse and their effect on the probe pulse. Expressions for the density-matrix jumps, induced by the probe pulse, have been obtained in a general case. The material equations, determining propagation of the probe pulse, have been derived.
In ultrashort (femtosecond) pump-probe spectroscopy, the pump pulse creates a nonstationary medium while the probe pulse propagates in such a medium. The analysis of this situation is performed in the framework of linear nonstationary optics. Constitutive equations and electrodynamics of the nonstationary media are analyzed. The propagation of the probe-pulse energy is characterized by the coarse-grained susceptibility introduced in the previous works of the authors [S. H. Lin and B. Fain, Chem. Phys. Lett. 157, 233 (1989); B. Fain, S. H. Lin, and N. Hamer, J. Chem. Phys. 91, 4485 (1989); B. Fain and S. H. Lin, Chem. Phys. 161, 515 (1992)]. The main objective of the paper is the derivation and analysis of the delay-time-dependent absorption and dispersion line shapes of the probe pulse. This line shape has a very specific form corresponding to phase-dependent Raman absorption (emission). The latter phenomenon is introduced and described in the present paper.
The coherence spike observed in the transmitted probe intensity decay curve in pump–probe experiments is analyzed with a model which depends explicitly upon the population decay and dephasing rate constants. Using this model and simple pulse shape functions a series of decay curves are calculated throughout the range of wide to narrow pulse widths relative to the dephasing time. These calculations suggest that the coherence spike may be used to obtain information about the phase coherence in the electronic or vibrational transition being investigated, when the pulse width is comparable to or smaller than the dephasing time. Methods of extracting T2 from the coherence spike are also discussed.
Two atoms in an ultracold gas are correlated at short interatomic distances due to threshold effects in which the potential energy of their interaction dominates the kinetic energy. The correlations manifest themselves in a distinct nodal structure of the density matrix at short interatomic distances. Pump-probe spectroscopy has recently been suggested [Phys. Rev. Lett. 103, 260401 (2009)] to probe these pair correlations: A suitably chosen, short photoassociation laser pulse depletes the ground-state pair density within the photoassociation window, creating a nonstationary wave packet in the electronic ground state. The dynamics of this nonstationary wave packet is monitored by time-delayed probe and ionization pulses. Here we discuss how the choice of the pulse parameters affects the experimental feasibility of this pump-probe spectroscopy of two-body correlations.
Recent femtosecond transmission-correlation measurements1 of large organic dye molecules revealed surprising details concerning the ultrafast relaxation dynamics of such dyes. Superposed on simple exponential decays, the observation of damped sinusoidal oscillations with a period of ~ 150 fs has been puzzling. We theoretically and numerically demonstrate that such oscillatory behavior could be due to quantum beats of closely spaced two levels, whose coherent superposition state is optically prepared and monitored by a pair of femtosecond pulses. Although studies of quantum beats have been developed in both fluorescence-type2 and nonfluorescence-type measurements, such as those based on photon echoes3 or polarization spectroscopy,4 this simple method gives a new approach to femtosecond time domain spectroscopy. The generalized perturbation theory5 of optical coherent transients is extended to the case of optical transmission-correlation or pump-probe-type experiments. The model used is a three-level system which has split levels in either the ground or optically excited states. Especially, if the ground state has sublevels, the system becomes quite similar to the case of coherent Raman beats. Both cases are shown to give quantum beats when the excitation pulses are short compared with the inverse sublevel splitting. The period and decay time of the damped sinusoid represent the separation energy and the dephasing time between the sublevels, respectively. Using third-order perturbation theory, the transmission-correlation signal STC(τ) as a function of the first-to-second pulse delay time Is derived for arbitrary-shaped excitation pulses and is given in the form of fourfold integrals with many terms.