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Global and Local Models for Dilution Factors: Theory and Stimulated Emission Pumping Experiments

Sandra Lee

Published Jan 1, 2005• 0 citations
OpenAlex

Abstract

The dilution factor is a measure of the intramolecular vibrational energy redistribution (IVR) an excited state undergoes. The distribution of dilution factors for a single molecule (SCCl2) was examined. Stimulated emission pumping (SEP) experiments were performed on SCCl2, probing the 7000--8,000 cm-1 range on the ground electronic state from first excited state and the 7,000--10,000+ cm-1 range from the second electronic state. An extended cross correlation analysis was applied to obtain more accurate measurements of dilution factors. Simulated SEP spectra were constructed according to two theoretical models: a globally random Golden Rule model and a locally random analytical model. Autocorrelation of the experimental and simulated differences revealed a simple and robust method of analyzing the distribution of dilution factors within a spectrum.

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The dilution factor is a measure of the intramolecular vibrational energy redistribution (IVR) an excited state undergoes. The distribution of dilution factors for a single molecule (SCCl2) was examined. Stimulated emission pumping (SEP) experiments were performed on SCCl2, probing the 7000--8,000 cm-1 range on the ground electronic state from first excited state and the 7,000--10,000+ cm-1 range from the second electronic state. An extended cross correlation analysis was applied to obtain more accurate measurements of dilution factors. Simulated SEP spectra were constructed according to two theoretical models: a globally random Golden Rule model and a locally random analytical model. Autocorrelation of the experimental and simulated differences revealed a simple and robust method of analyzing the distribution of dilution factors within a spectrum.
The development of accurate tools to characterize Intramolecular Vibrational Redistribution (IVR) is of major interest in chemistry. In this context, surface-enhanced vibrational spectroscopies stand up as well-established techniques to study molecular vibrational lines and populations with a sensitivity that can reach the single-molecule level. However, to date, this possibility has not been fully developed to address IVR. Here, we establish a quantum mechanical framework based on molecular optomechanics that accounts for IVR, and we adopt it to analyze strategies to optimize IVR characterization by surface-enhanced vibrational spectroscopy. In particular, we model two different pump-and-probe configurations where the vibrational pumping is provided either by infrared laser illumination or by Stokes scattering processes in surface-enhanced Raman spectroscopy (SERS). We show for the two pumping configurations the existence of clear signatures on the anti-Stokes SERS spectra of population transfer between coupled vibrational modes in a molecule. Our calculations adopt realistic molecular and SERS parameters, suggesting that these signatures of IVR could be accessible at the single-molecule level within realistic experimental platforms.
A theory of the photon echo is presented for excitation of the vibrational–rotational transitions in a polyatomic molecule followed by the process of intramolecular vibrational redistribution (IVR). A model is considered that includes a description of IVR using the general statistical properties of chaotic states rather than phenomenological. Special attention is paid to the echo signals at the delay times that are considerably larger than the characteristic times of IVR. It is shown that echo measurements for the far plateau of the IVR curve can provide, directly or indirectly, determination of the so-called dilution factors; their values are of primary importance for estimating effective density of the molecular states that participate in IVR. Differences between the echo and anti-Stokes Raman scattering, really used for the same purposes, are discussed.
The interaction of two narrow band (Δν<100 MHz) UV light pulses of different intensity with a molecular three-level system is investigated experimentally. The laser frequencies are tuned to an up (pump) and a down (dump) transition sharing a common excited rovibronic S1 level whose population is probed by a transition to the ionization continuum and ion detection. The time sequence of the two pulses results either in a lambda type coherent stimulated Raman adiabatic passage or a stimulated emission pumping (SEP) process. When the first case is realized by a 6.4 ns delay of the low intensity pump laser from the high intensity dump laser pulse, a fourfold increase of the depth of the ion dips compared to the SEP experiment is observed. This is in line with numerical calculations of the level populations using a density matrix formalism including coherent effects. Rotationally resolved ion dip spectra of the 62 state of benzene are presented and demonstrate the high sensitivity of the coherent excitation process of this work for ion dip spectroscopy.
We report a fully quantum-dynamical study of the intramolecular vibrational energy redistribution (IVR) in the electronic ground state of carbonyl sulfide, which is a prototype of an isolated many-body quantum system with strong internal couplings and non-Rice-Ramsperger-Kassel-Marcus (RRKM) behavior. We pay particular attention to the role of many-body localization and the approach to thermalization, which currently are topics of considerable interest, as they pertain to the very foundations of statistical mechanics and thermodynamics. We employ local-mode (valence) coordinates and consider initial excitations localized in one local mode, with energies ranging from low to near the dissociation threshold, where the classical dynamics have been shown to be chaotic. We propagate the nuclear wavepacket on the potential energy surface by means of the numerically exact multiconfiguration time-dependent Hartree method and employ mean local energies, time-dependent and time-averaged populations in quantum number space, energy distributions, entanglement entropies, local population distributions, microcanonical averages, and dissociation probabilities, as diagnostic tools. This allows us to identify a continuous localization → delocalization transition in the energy flow, associated with the onset of quantum chaos, as the excitation energy increases up to near the dissociation threshold. Moreover, we find that at this energy and ∼1 ps the molecule nearly thermalizes. Furthermore, we observe that IVR is so slow that the molecule begins to dissociate well before such quasi-thermalization is complete, in accordance with earlier classical-mechanical predictions of non-RRKM behavior.
The technique of stimulated emission depletion of fluorescence (STED) from a two photon excited molecular population is demonstrated in the S1 excited state of fluorescein in ethylene glycol and methanol. Two photon excitation (pump) is achieved using the partial output of a regeneratively amplified Ti:Sapphire laser in conjunction with an optical parametric amplifier whose tuneable output provides a synchronous depletion (dump) pulse. Time resolved fluorescence intensity and anisotropy measurements of the fluorescein emission are made using picosecond time-correlated single photon counting. Pump-dump time delayed fluorescence intensity measurements are used to characterise the response of the system and to provide additional data on saturation dynamics of the dump transition. Two photon STED is modelled using both approximate analytical techniques in the weak dump limit and by numerical solutions to the appropriate rate equations. The latter are used to fit experimental data from which it is possible to determine the cross-section for the stimulated transition and lifetime of the upper vibrational levels of the ground state.
In two recent works, the authors have investigated the spectro-temporal properties of the random laser emission from solid state dye-doped powders in picosecond pumping regime. Each emission pulse consists, both above and below threshold, in a collection of narrow peaks of a spectro-temporal width at the theoretical limit (ΔωΔt≅1). The distribution of path lengths traveled inside the diffusive active medium by photons that can be amplified by stimulated emission explains this behavior, as demonstrated by a simple theoretical model developed by the authors. The aim of the present work is, first, to develop an implemented model that does not depend on fitting parameters, and which is compatible with the energetic and spectro-temporal properties of the material; and second, to get knowledge about the spatial properties of the emission. The transverse coherence size of each emitted photon packet has been measured; and in addition, we have shown the existence of spatial fluctuations of the emission of these materials, as our model predicts.