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Physical review. B, Condensed matter

Effects of spectral diffusion in incoherent photon-echo experiments

Yue Bai, M. D. Fayer

Published Jun 15, 1988• 21 citations
Publisher

Abstract

The application of the incoherent photon-echo experiment to complex systems is analyzed. In systems in which spectral diffusion occurs, incoherent echo measurements do not yield the same optical dephasing rate as conventional two-pulse photon-echo measurements. The difference can be of major significance. To make the calculations explicit, optical dephasing in a glass is considered using the tunneling two-level system model.

DOI
10.1103/physrevb.37.10440

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The application of the incoherent photon-echo experiment to complex systems is analyzed. In systems in which spectral diffusion occurs, incoherent echo measurements do not yield the same optical dephasing rate as conventional two-pulse photon-echo measurements. The difference can be of major significance. To make the calculations explicit, optical dephasing in a glass is considered using the tunneling two-level system model.
We have observed a significant ``instantaneous spectral diffusion'' phenomenon in photon-echo experiments on Tb3+{\mathrm{Tb}}^{3+}Tb3+:LiYF4{\mathrm{LiYF}}_{4}LiYF4​. This laser-induced effect makes observed optical dephasing rates intensity dependent and can also contribute a frequency dependence to the measured rates. A change in the magnetic dipole-dipole interaction between Tb3+{\mathrm{Tb}}^{3+}Tb3+ echo ions and surrounding Tb3+{\mathrm{Tb}}^{3+}Tb3+ ions occurs when surrounding ions are excited. This causes an instantaneous shift in the optical frequency of the echo ion that lasts for T1{\mathit{T}}_{1}T1​\ensuremath{\sim}1 msec. Frequency shifts caused by the first excitation pulse have no effect on echo rephasing (T1{\mathit{T}}_{1}T1​\ensuremath{\gg}T2{\mathit{T}}_{2}T2​), but those caused by the second pulse prevent proper echo rephasing. A summary is given of other ion-lattice and ion-ion interactions that can cause similar laser-induced effects in a wide variety of insulating compounds. There is potential for probing the nature of inhomogeneous broadening.
The long-lived stimulated photon echo is put forward as a powerful technique to probe structural dynamics in glasses and other amorphous solids. We present results of optical dephasing measurements on several doped organic glasses (deuterated ethanol, toluene, and triethylamine) and polymers (polystyrene, polyvinylbutyral, and polymethylmethacrylate). Using a stochastic analysis within the so-called two-level-system model, we can extract from these measurements the distribution function of fluctuation rates over a huge range of time scales, varying from picoseconds to hundreds of milliseconds. We show that the dynamics, which lies at the origin of spectral diffusion, is very dependent on the glass structure and can be described by two separate hyperbolic distribution functions of fluctuation rates. From longitudinal photon echo measurements in the population dimension, we find evidence for structural dynamics which is not accounted for in the standard two-level-system model and which is related to a spatially inhomogeneous distribution of fluctuation centers.
Picosecond photon echo (PE) experiments are used to examine the optical dephasing and intermolecular interactions of organic chromophores in a variety of glassy organic and polymer hosts. The inherent disorder in these systems leads to dynamics which span times from picoseconds to hours and longer. The temperature dependent optical dephasing as measured by the PE follows a power law characteristic of tunnelling twolevel systems (TLS) at low temperatures (1 °K to 4 °K) and is exponentially activated at higher temperatures due to dephasing by additional modes. The nature of these modes will be addressed. These data and those from other line narrowing experiments such as hole burning allow the study both of fast dephasing processes and spectral diffusion due to slow fluctuations in the host. The observed lineshapes and holewidths require dipolar coupling between the chromophore and TLS and offer information on the distribution of relaxation rates. Furthermore, techniques sensitive to different timescales are used to examine host dynamics by removing the guest-host coupling from consideration. The data are discussed in conjunction with recently developed theoretical treatments of dephasing in disordered systems.
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.