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Physical Review A

General theory of temperature-dependent ultrafast transient hole burning

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

Published Nov 1, 1992• 5 citations
Publisher

Abstract

In this paper, we report the theoretical treatment of ultrafast time-resolved hole burning. The description is valid for nonoverlapping and overlapping pulses as well. Also the effects of the temperature are included in the theory. The influence of the various contributions to the transient hole-burning spectrum corresponding to the level population, pump polarization coupling, and perturbed free-induction-decay terms is stressed.

DOI
10.1103/physreva.46.5959

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In this paper, we report the theoretical treatment of ultrafast time-resolved hole burning. The description is valid for nonoverlapping and overlapping pulses as well. Also the effects of the temperature are included in the theory. The influence of the various contributions to the transient hole-burning spectrum corresponding to the level population, pump polarization coupling, and perturbed free-induction-decay terms is stressed.
A model calculation is presented that describes the features of spectral-hole burning measurements performed under conditions of femtosecond transient excitation and probing. Pump-induced changes in the spectrum of probe transmittance arise not only from changes in level population (hole burning), but also from the presence of pump polarization during the probe, and from perturbations of the decay of the probe polarization. These latter effects give rise to oscillating differential transmittance spectra when the (shorter) probe pulse arrives prior to the peak of the pump noise. Only when the probe pulse follows the bulk of the pump pulse does the level population effect dominate the spectrum, so that one can observe dynamic hole-burning effects without distortion.>
Theory based on a configuration coordinate model is presented to clarify solute–solvent relaxation effect on the line shape of a time-resolved hole-burning spectrum. The time-resolved hole-burning spectrum is affected by both a hole created in a ground-state population and an excess excited-state population. The solute–solvent relaxation causes thermalization in both populations and then the shift and broadening of the spectrum is expected observable. The line shapes of three typical cases are mainly considered: (1) The excited state is assumed to have an infinitely long lifetime; (2) the excited state has a finite lifetime, the population being assumed to relax toward an electronic state other than the ground state, and (3) the population created in the excited state relaxes to the ground state, where a hole-filling effect is taken into account. Results obtained by numerical calculations show that a time evolution of the ground-state hole is clearly observed when the low-energy tail of the absorption band is excited under the condition that the population decay to the other electronic state is very fast. Further, it is predicted that the hole-filling effect causes a considerable deformation of the spectral shape when the solvent relaxation rate is comparable to the excited-state population decay rate.
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.
A consistent explanation of recent studies by Szabo and Muramoto [Phys. Rev. A 39, 3992 (1989); 38, 5928 (1988)] on the experimental test of modified optical Bloch equations is presented. It is shown that the observed peculiarities of optical transients in solids are connected with the mechanism of relaxation in systems with slow stochastic modulation. A theory of laser-modified relaxation and analysis of free induction decay (FID), hole burning, and rotary echo (RE) in such systems are presented. The universal character of the FID time dependence and field-independent RE decay is predicted.
In this paper theories are given, describing photophysical and photochemical hole burning experiments on molecular mixed crystals at low temperature. Population saturation hole burning is treated for a two-level system where the lower level is the ground state. Hole burning due to a triplet state acting as a population bottle neck is also described by a steady-state density matrix theory. Connection is made with optical free induction decay. To obtain T2 (the decay time of the off-diagonal elements of the density matrix), which is the main goal of these hole burning experiments, a linear extrapolation method is discussed. For photochemical hole burning a time-dependent density matrix treatment is given. Using this theory numerical simulations were performed of the experimental results obtained by Völker and co-workers for porphin in n-octane at low temperature. Good agreement with experiment is obtained. For this case extrapolation methods are discussed in order to obtain reliable T2 values. A time-dependent kinetic theory is used to simulate the photochemical hole burning experiments on dimethyl-s-tetrazine in durene and s-tetrazine in benzene. This theory accounts for the recently revealed two-photon character of these photodissociations. It is shown that despite this complication the hole full width at half-maximum may still equal twice the homogeneous width of the So-S1 transition.