A theory of optical echo spectroscopies of large polyatomic molecules in condensed phases is developed. Using phase space correlation functions, we examine the interrelationships among the following optical measurements: ordinary photon echo, stimulated photon echo, accumulated photon echo, incoherent accumulated photon echo, and pump–probe absorption. Conditions for the elimination of inhomogeneous broadening in these experiments are specified. A multimode Brownian oscillator model is used to account for high frequency molecular vibrations, as well as solvent modes, and electronic dephasing processes. The effects of quantum beats, spectral diffusion, and homogeneous dephasing on the echo signals are studied and compared in detail with pump–probe and hole burning spectroscopy.

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Photon echoes of polyatomic molecules in condensed phases

The magnitudes, time scales, and underlying mechanisms responsible for broadening the electronic spectra of molecules in liquid solutions and glasses are reviewed. The emphasis is on experimental results from hole-burning, single-molecule, photon echo, and resonance Raman and fluorescence studies. The influence of the time scale of the measurement in distinguishing between homogeneous broadening (electronic dephasing) and inhomogeneous broadening is discussed, and the role of coupling of solvent phonons to the solute's electronic transition is stressed.

Molecular electronic spectral broadening in liquids and glasses.

A detailed theoretical analysis of optical dephasing measurements performed on complex systems, e.g., glasses, proteins, or complex crystals, is presented. Unlike simple crystals, such systems undergo dynamical processes which have a very broad rate distribution. Dynamics can occur on a variety of time scales ranging from subpicoseconds to seconds, or longer. The formalism is based on a four-point correlation-function description of line-narrowing experiments. The results of optical dephasing measurements (time domain) or linewidth measurements (frequency domain) depend on a time ${T}_{W}$ which defines the time scale associated with the particular experimental technique. Detailed information about the rate distribution of the system's dynamics is obtained from the change in the optical dephasing rate as the experimental time scale is changed, not from the dephasing rate measured in any individual experiment. A fundamental result, which is independent of the nature of the rate distribution or the coupling to the optical center, is proven; i.e., the derivative of the optical dephasing rate with respect to ${T}_{W}$, the experimental time scale, is directly proportional to the Laplace transform of the fluctuation rate distribution. As examples, the formal results are applied to two types of systems, optical centers in a glass and in a complex crystal. For the crystalline system ${\mathrm{Pr}}^{3+}$:${\mathrm{CaF}}_{2}$, ${T}_{W}$-dependent optical dephasing data from the literature are analyzed quantitatively, where previously only a qualitative description was possible.

Time scales and optical dephasing measurements: Investigation of dynamics in complex systems.

We develop a theory of photon‐echo phenomena in harmonic vibrational modes. Although classical harmonic oscillators cannot produce any nonlinear optical signal in the linear response limit, we demonstrate that quantum harmonic oscillators that are coupled to any physically reasonable bath can give rise to novel nonlinear optical behavior, even in the perturbative limit. We show that photon echoes in high‐frequency vibrational modes are strongly affected by both population relaxation and pure dephasing. The time dependence of the echo signal is shown to be highly sensitive to the amount of inhomogeneous broadening in the vibrational line. As an example, we develop the simple model of population relaxation resulting from linear coupling to the bath and pure dephasing resulting from quadratic coupling to the bath. Counter to the classical picture, echo signal is present when the only coupling to the bath is linear, but absent when the only coupling is quadratic.

Theory of nonlinear optical experiments with harmonic oscillators

Results of picosecond photon echo and optical hole burning experiments are reported for four ionic dyes in ethanol glass. At low temperatures, the dephasing times deduced from the hole widths are as much as nine times shorter than those measured by the two‐pulse echo because of the effect of spectral diffusion. The temperature dependences found are of the form aTα+b exp (−ΔE/kT) due to glass two level system dynamics (T<4 K) and a process that activates exponentially at higher temperatures, possibly from a pseudolocal mode or glass optical phonon. Comparing the ratios of echo to hole burning measured dephasing times for the four dyes suggests that the dephasing is influenced by the existence of distinct local ethanol solvation shells in addition to the dynamics of the bulk solvent. A theoretical description of solvent shell effects is achieved through the use of a two spatial domain model of the glass dynamics. Calculations of dynamic perturbations from distinct solvation shell and bulk solvent regions sh...

Solvation shell effects and spectral diffusion: Photon echo and optical hole burning experiments on ionic dyes in ethanol glass

http://web.stanford.edu/group/fayer/articles/104.pdf

Optical dephasing in glasses: theoretical comparison of the incoherent- photon echo, accumulated grating echo, and two-pulse photon echo experiments

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Optical dephasing in glasses: theoretical comparison of the incoherent- photon echo, accumulated grating echo, and two-pulse photon echo experiments