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Physical Review A

Non-Markovian effects on optical absorption

A. A. Villaeys, J. C. Vallet, S. H. Lin

Published May 1, 1991• 19 citations
Publisher

Abstract

In this paper, we shall report the investigation of the non-Markovian effects of the dynamical process on optical absorption. It will be shown that in steady-state experiments the non-Markovian effects cannot be probed. The non-Markovian effects on the transient pump-probe experiment are treated, and a couple of typical memory functions have been used to obtain the transient band-shape functions. Finally, probe-pulse duration effects on the absorption are considered.

DOI
10.1103/physreva.43.5030

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In this paper, we shall report the investigation of the non-Markovian effects of the dynamical process on optical absorption. It will be shown that in steady-state experiments the non-Markovian effects cannot be probed. The non-Markovian effects on the transient pump-probe experiment are treated, and a couple of typical memory functions have been used to obtain the transient band-shape functions. Finally, probe-pulse duration effects on the absorption are considered.
The influence of transverse relaxation on the resonance soliton ($2\ensuremath{\pi}$ hyperbolic-secant pulse) in solids is considered. It is shown that memory effects can be considered in terms of generalized non-Markovian optical Bloch equations. The equations of self-induced transparency with a memory function are presented. Explicit forms for the first-order effects of this relaxation on the frequency shift and the pulse height of a resonant $2\ensuremath{\pi}$ soliton in solids are given and discussed. It is shown that memory effects do lead to a qualitative change in the dynamics of the influence of transverse relaxations on a $2\ensuremath{\pi}$ pulse in comparison to the McCall-Hahn theory and others. The dynamics of the changes of the inverse width of the pulse are obtained in both the Markovian and the non-Markovian cases with realistic parameters that can be achieved in current experiments.
Based on the standard system-heat-bath model, we have formulated a theory of the non-Markovian master equation for linear and nonlinear systems for a correlation time that is short but finite. We have applied the theory to linear systems, such as harmonic oscillators and two-level atoms and calculated the band-shape functions for transient optical absorption in the pump-probe experiments. The significant interplay of nonlinearity and non-Markovian decay has been illustrated by another application of the theory to a Morse oscillator. The theory is valid for arbitrary nonlinearity and finite temperatures but within the weak-coupling limit and has been derived without ad hoc implementation of a phenomenological memory function.
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].
Femtosecond photon-echo experiments on sodium resorufin in dimethylsulfoxide at room temperature show that optical dephasing in solution is of non-Markovian character. A single Gauss-Markov stochastic modulation process is used to interpret both the femtosecond light-scattering results and the steady-state absorption spectrum. The optical dynamics of this system appears to fall in the intermediate modulation regime. No evidence was found for contributions of slower dynamical processes to the absorption line breadth.
The physical interpretation of time-resolved photoabsorption experiments is not as straightforward as for the more conventional photoabsorption experiments conducted on equilibrium systems. In fact, the relation between the transient photoabsorption spectrum and the properties of the examined sample can be rather intricate since the former is a complicated functional of both the driving pump and the feeble probe fields. In this work, we critically review the derivation of the time-resolved photoabsorption spectrum in terms of the nonequilibrium dipole response function $\ensuremath{\chi}$ and assess its domain of validity. We then analyze $\ensuremath{\chi}$ in detail and discuss a few exact properties useful to interpret the transient spectrum during (overlapping regime) and after (nonoverlapping regime) the action of the pump. The nonoverlapping regime is the simplest to address. The absorption energies are indeed independent of the delay between the pump and probe pulses and hence the transient spectrum can change only by a rearrangement of the spectral weights. We give a close expression of these spectral weights in two limiting cases (ultrashort and everlasting monochromatic probes) and highlight their strong dependence on coherence and probe envelope. In the overlapping regime, we obtain a Lehmann-type representation of $\ensuremath{\chi}$ in terms of light-dressed states and provide a unifying framework of various well-known effects in pump-driven systems. We also show the emergence of spectral substructures due to the finite duration of the pump pulse.
We show that in order to describe completely the coherent coupling between the pump and probe pulses in a pump– probe measurement of transient absorption, the influence of induced phase gratings must be included. The importance of phase gratings is demonstrated experimentally for the case of a bleachable dye and analyzed in terms of transient four-wave mixing. These results are relevant to the interpretation of pump–probe measurements on all time scales performed with pulses from a single laser, particularly when the pulse duration is comparable with the material response time.