Non-Markovian dephasing of molecules in solution measured with three-pulse femtosecond photon echoes

Abstract

The electronic dephasing of large molecules in solution is investigated with three-pulse photon echoes generated by 6-fs optical pulses. The observed dephasing behavior, which is analyzed with a model based on a stochastic coupling of the molecules with their heat bath, is clearly shown to be non-Markovian. Moreover, the correlation function of the fluctuations asymptotically approaches an exponential with characteristic times varying from 20 to 80 fs, depending on the solvent environment.PACS numbers: 42.50.Md Ultrafast spectroscopy performed with femtosecond optical pulses has provided important new information on the nature of the optical absorption of large dye molecules in solution. Spectral hole-burning and coherent transient measurements have been used to determine the degree of inhomogeneity of the optical-absorption spectrum and the appropriate statistical description of the molecule in its solvent environment. Hole-burning experiments 1 and two-pulse photon-echo experiments 2 have clearly shown the large molecules Nile Blue and Malachite Green to be inhomogeneously broadened. In this paper we present experimental results and analysis which go beyond the interpretation of the data in terms of a relaxation-time approximation to directly measure the frequency fluctuation correlation function with a threepulse photon-echo technique using 6-fs optical pulses.Weiner, Silvestri, and Ippen 3 have previously attempted to measure a three-pulse photon echo using pulses an order of magnitude longer than those used in this experiment, but were unable to resolve the polarization dephasing. Rosker, Wise, and Tang 4 and Chesnoy and Mokhtari 5 have observed what they term "quantum beats" using transient absorption spectroscopy. Although these experiments were originally interpreted in terms of coherence between electronic levels in the dye molecules, recent measurements 6 and theory 7 have shown that the observed oscillations are the result of wave-packet motion brought about by the coherent excitation of the manifold of vibrational levels. Most recently, Nibbering, Duppen, and Wiersma 8 studied optical dephasing in solution using line-shape analysis and resonance light-scattering measurements.We use femtosecond optical techniques to study the interactions of the dye molecule with its environment and the mechanisms responsible for the loss of electronic coherence. Such interactions may be explicitly analyzed by molecular-dynamic simulations, but usual tractable models collect all the degrees of freedom of the solute and solvent into a coupling with a thermal bath. With this type of description, the dephasing behavior of the molecules is determined by the statistical properties of the molecule-heat-bath coupling. The simplest model of a dephasing process assumes that the correlation time T C of the fluctuations of the molecule electronic gap is much shorter than Ti (the limit r c =0 corresponds to the particular Markovian case of a ^-correlation function). In general, the statistics are more complicated and may or may no...

The dynamics of one-dimensional excitons in liquids

“…6 are longer than ever measured before in a room temperature liquid. [20][21][22][23][24][25][26] The reason for this slow optical dephasing is the motional averaging of the exciton over the energetic perturbations, caused by the rapid motions of the molecules in the liquid. Unfortunately, we have no information of the optical dephasing of TDBC monomers to evaluate the averaging process quantitatively.…”

“…We therefore have to conclude that the optical dynamics of the TDBC-aggregates in water has to be described in a non-Markovian way, just as was found for single molecules in liquids. 21,22 The absorption spectrum A͑ ͒ can be calculated by summing over the various transitions from the ground state to the one-exciton band, each broadened by the optical dynamics…”

“…The single-molecule energy levels are subject to very rapid perturbations from the solvent molecules. For individually solvated molecules this leads to ultrafast dephasing of the optical transitions, which was in recent years extensively studied by a number of ultrafast techniques, such as transient hole burning, 19 two-and three-pulse photon echoes, [20][21][22][23][24][25][26] and chirped four-wave mixing. 27,28 For aggregates, the fluctuations lead to optical dephasing of the exciton optical transitions, and in addition they lead to localization of the excitation.…”

Wave Packet Dynamics in Ultrafast Spectroscopy of the Hydrated Electron

“…1 In the past decade, molecular dynamics simulation studies and ultrafast experiments on dye solutions have unearthed the basic picture of the solvation process as well as the relevant time scales. [2][3][4][5][6][7][8][9][10] Important aspects of the early-time dynamics, however, remained questionable, because it was not clear how the intramolecular vibrational dynamics could be separated from the solvation dynamical process itself. 8,10 Recently it was shown that comparative studies on the same dye in different solvents can distinguish between the two processes.…”

Mode suppression in the non-Markovian limit by time-gated stimulated photon echo

“…7,8 Another sensitive probe of solvation dynamics is femtosecond ͑stimulated͒ photon echo. [10][11][12][13][14][15][16][17][18][19][20][21] The decay of this echo is used to obtain a nonlinear response function from which a solvation correlation function can be constructed. Although photon echo is a more indirect probe of solvation dynamics than time-gated fluorescence, its time resolution is superior because it is only set by the optical pulse length.…”