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physica status solidi (b)

Electronic Coherence Effects in Absorption Saturation Experiments

Reinhard Scholz, A. Stahl

Published Sep 1, 1992• 6 citations
Publisher

Abstract

Abstract In pump‐probe experiments with femtosecond pulses, a coherent peak is found in the absorption saturation for short pulse delays. This coherent peak is analysed within a density matrix model, including a realistic multi‐valence band structure and the optical matrix elements to leading order. Dissipative processes are treated in a relaxation time approximation. The parameters of the model are determined by comparison to experimental results.

DOI
10.1002/pssb.2221730120

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Abstract In pump‐probe experiments with femtosecond pulses, a coherent peak is found in the absorption saturation for short pulse delays. This coherent peak is analysed within a density matrix model, including a realistic multi‐valence band structure and the optical matrix elements to leading order. Dissipative processes are treated in a relaxation time approximation. The parameters of the model are determined by comparison to experimental results.
In some pump–probe optical correlation experiments, the measured signal versus delay between pulses generally consists of two components: the convolution of the pulse autocorrelation with the sample impulse response, and a coherent artifact. The latter can obscure the first component near zero delay where fast time scale processes will be manifest. We present a mathematical description of the relative shapes and sizes of the two components, so that a fitting process can separate them. This can yield both the dephasing and relaxation times of saturable absorbers such as semiconductors. The method is particularly appropriate when the orientational dephasing and relaxation times are of the same time scale as the laser pulse width.
The coherent excitation of a Wannier-exciton system by a short resonant light pulse is described through a simple model that takes into account explicitly the phase-space-filling effects due to the fermion nature of the electrons and holes composing the excitons. This formalism can describe both coherent-transient experiments, such as photon echoes, and optical observations at time scales longer than dephasing, such as absorption saturation. At high excitation densities the optical response of hydrogenic excitons deviates significantly from the response of the two-level model used traditionally to describe resonant effects. This suggests that coherent-optical-transient experiments, such as photon echoes, may be used to probe exciton interactions due to their internal structure, in addition to the relaxation processes that they probe in traditional experimental arrangements.
The dependence of the electronic absorption spectrum of a dye molecule on the time of delay between the excitation of the molecule by a pump-laser pulse and the probing of the absorption by a test-laser pulse is studied. The effect of dephasing of the molecular transition arising from the interaction with dissipative systems is described by a stochastic modulation of the electronic transition frequency. It is shown that in the case when the two laser pulses are short compared with the correlation time of the frequency modulation and when the spectral linewidth of the pump-laser light is smaller than the bandwidth of the equilibrium absorption spectrum, hole burning appears although the molecules have equal mean transition frequencies. This effect arises from non-Markovian correlations between the dephasings of the molecule during the actions of the pump- and the test-laser pulse. With increasing delay time the holes are smoothed out and disappear when the delay time exceeds the correlation time. Such effects were found in recent femtosecond absorption experiments by Shank et al. [in Ultrafast Phenomena V, dited by G. R. Fleming and A. E. Siegman (Springer, Berlin, 1986), p. 179].
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 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.