Roger F. Loring

Time‐resolved fluorescence and hole‐burning line shapes of solvated molecules: Longitudinal dielectric relaxation and vibrational dynamics

We develop a microscopic theory of time‐ and frequency‐resolved fluorescence and hole‐burning measurements of polar, polyatomic molecules in a polar solvent. The line shapes are expressed in terms of gas phase spectroscopic parameters of the solute, vibrational relaxation rates, laser pulse shapes, and the dynamics of a solvation coordinate. These dynamics are then related to the frequency and wave vector dependent dielectric function of the solvent. Both fluorescence and hole‐burning line shapes are predicted to show significant line narrowing at short times, and to undergo broadening and a red shift as the solvent relaxes. We propose hole burning as an alternative to fluorescence measurements in probing solvation dynamics. The time scale of the solvent induced line shift and line broadening is found to be independent of the shape of the solute, in contrast with previous work. The effects of vibrational relaxation are distinguished from those of solvent relaxation.

Nonlinear response function for time-domain and frequency-domain four-wave mixing

A unified theory of time-domain and frequency-domain four-wave mixing processes, which is based on the nonlinear response function R(t3, t2, t1), is developed. The response function is expressed in terms of the four-point correlation function of the dipole operator F(τ1, τ2, τ3, τ4) and is evaluated explicitly for a stochastic model of line broadening that holds for any correlation time of the bath. Our results interpolate between the fast-modulation limit, in which the optical Bloch equations are valid, and the static limit of inhomogeneous line broadening. As an example of the relationship between time-domain and frequency-domain four-wave mixing, we compare the capabilities of steady-state and transient coherent anti-Stokes Raman spectroscopy experiments to probe the vibrational dynamics in ground and excited electronic states.

Selectivity in coherent transient Raman measurements of vibrational dephasing in liquids

The microscopic information content of coherent transient Raman measurements is analyzed. It is shown that for short pulses and optically thin samples the Kaiser–Laubereau pulse sequence is the Raman analog of the optical free induction decay, and that the experimental observable contains the same dynamical information as the isotropic, spontaneous Raman line shape. Under these conditions, the experiment therefore cannot be used to selectively measure the homogeneous dephasing time of a system with an inhomogeneously broadened line. The results of our analysis are at variance with the earlier results of Kaiser and Laubereau and the more recent predictions of Oxtoby. However, these experiments, under certain circumstances, may be used to obtain a nonselective line narrowing, as found by Zinth, Polland, Laubereau, and Kaiser. We also consider the situation in which the sample is optically dense, in which case laser depletion must be taken into account. The distinction between saturation of the vibrational t...

Molecular theory of solvation and dielectric response in polar fluids

The response of a polar fluid to an electric field of arbitrary spatial and temporal characteristics is considered. Microscopic expressions are derived for the transverse and longitudinal dielectric functions eT (k,ω) and eL (k,ω). The notions of ‘‘transverse relaxation time’’ and ‘‘longitudinal relaxation time’’ are discussed and clarified. We propose an algorithm, by which data from macroscopic dielectric relaxation measurements, which probe the dielectric response at long wavelengths, may be used to predict the dielectric response of a polar fluid on molecular length scales. We construct a partially resummed density expansion of the polarization response of a model system composed of interacting dipoles which undergo rotational Brownian motion. Numerical calculations are given of the temporal and spatial behavior of the polarization induced in this system by the sudden introduction of a point charge.

Unified theory of photon echoes: The passage from inhomogeneous to homogeneous line broadening

Abstract We calculate the temporal profile of the photon echo signal from a collection of non-interacting two-level systems. whose frequencies undergo Gaussian random modulations. The model is exactly solvable and interpolates continuously between the inhomogeneous broadening limit in which a well-defined echo signal exists and the homogeneous broadening limit in which it is no longer present. The implications for the problem of concentration-dependent dephasing in mixed molecular crystals are discussed.

Time- and frequency-resolved fluorescence line shapes as a probe of solvation dynamics

Abstract The time- and frequency-resolved fluorescence spectrum of a polar molecule in a polar solvent is expressed in terms of gas phase spectroscopic parameters of the solute, vibrational relaxation rates, the dielectric properties of the solvent, and the temporal profile of the excitation pulse. The fluorescence spectrum is narrow at short times, and displays line broadening and a red-shift as the solvent relaxes about the excited solute.

Microscopic theory of the transient grating experiment

We present the first fully microscopic theory of the generation of the transient grating signal from a crystal of interacting molecules. We derive a general expression for the signal, measured at a time immediately after a short probe pulse, in terms of the exciton Green function. This expression agrees with previous calculations of the grating signal, in which the experiment was treated as a diffraction process. It is also shown that the temporal profile of the signal pulse is, in general, different from that of the probe pulse. This result is inconsistent with the usual diffraction picture. Our treatment of this experiment as a transient four‐wave mixing process rather than as a diffraction process allows us to derive an expression for the signal in terms of equilibrium correlation functions of the dipole operator. Using this formulation, we discuss the relationship of this experiment to other nonlinear spectroscopic techniques.

Extra resonances in four‐wave mixing as a probe of exciton dynamics: The steady‐state analog of the transient grating

We present a microscopic theory of the nonlinear susceptibility χ(3) of a crystal composed of interacting two‐level absorbers. The relationship between the signals in a steady‐state four‐wave mixing experiment and in a time‐resolved transient grating experiment is established. In general, the steady‐state signal is not simply the Fourier transform of the time‐resolved signal, although such a relationship does hold under certain experimental conditions. We evaluate χ(3) for the Haken–Strobl model. χ(3) displays a dephasing‐induced extra resonance, whose intensity and line shape are sensitive to the degree of exciton coherence. We also calculate χ(3) for a crystal of interacting three‐level absorbers, under the assumption that population in the higher excited state relaxes rapidly to the lower excited state. We propose steady‐state four‐wave mixing as an alternative to the transient grating experiment in investigating the nature of exciton motion.

Effective dephasing theory of the optical Anderson transition as probed by four‐wave‐mixing spectroscopy

A novel theory of quantum mechanical transport in disordered systems is developed. The theory is based on the effective dephasing approximation (EDA), in which the ensemble averaged Liouville space propagator is mapped into the propagator of an ordered lattice with an effective frequency‐dependent dephasing rate. This generalized dephasing rate is determined self‐consistently. This approach is applicable to strongly disordered systems and yields results that interpolate between the limits of coherent and incoherent excitation transport and that predict the optical analog of a metal–insulator phase transition (Anderson localization). Our results agree with the predictions of the scaling theory of the Anderson transition. We apply the EDA to the calculation of the transient grating signal from a crystal with an inhomogeneously broadened absorption spectrum (static, site energy disorder). The transient grating experiment is shown to be a sensitive probe of the optical Anderson transition.

Theory of carrier motion in dynamically disordered systems

We present a quantum mechanical theory of the dynamics of a charge carrier or an electronic excitation in a condensed phase system, in which the solvent degrees of freedom that couple to the electronic excitation are characterized by a correlation time of arbitrary magnitude. We consider a charge carrier moving among active sites that are randomly distributed in space. The site energies undergo stochastic modulation with a finite correlation time, through the interactions with the solvent. A mode‐coupling self‐consistent equation is derived from which transport properties such as the ac conductivity, the mean‐squared displacement, and the time‐dependent probability that a carrier remains on the initial site are calculated. A metal–insulator transition is predicted in three dimensions, but not in one or two dimensions, in agreement with the scaling theory of Anderson localization. The present treatment allows the investigation of carrier dynamics even when there is no separation of time scales between the ...