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Physical review. B, Condensed matter

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

Yu Bai, M. D. Fayer

Published May 15, 1989• 124 citations
Publisher

Abstract

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.

DOI
10.1103/physrevb.39.11066

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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 TW{T}_{W}TW​ 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 TW{T}_{W}TW​, 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 Pr3+{\mathrm{Pr}}^{3+}Pr3+:CaF2{\mathrm{CaF}}_{2}CaF2​, TW{T}_{W}TW​-dependent optical dephasing data from the literature are analyzed quantitatively, where previously only a qualitative description was possible.
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.
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A general description of zero-temperature pure dephasing in optical multilevel systems is presented. We derive expressions for the dephasing time due to transition multipole interactions. Specific application of the theory to mixed crystal systems predicts the dependence of the dephasing times on the concentration of guest molecules and transition dipole moments which is observed experimentally. Numerical estimates of the zero-temperature dephasing rates are in good agreement with experiments when the dependence on exciting pulse flip angle is included. Finally, our results suggest new experiments which are briefly discussed.
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Photons are useful quantum systems for investigating the fundamental and practical aspects of dephasing, decoherence, and other types of open quantum dynamics. However, descriptions of open dynamics of photonic systems are usually in terms of decoherence functions and in many cases an explicit master-equation-based description is not available. This is particularly true when considering multipartite photonic open systems having possibly correlated environments. We obtain generic master equations for the reduced dephasing dynamics of a two-photon polarization state coupled to respective frequency degrees of freedom when the frequency degrees of freedom that form the environment are initially correlated. Our results show the explicit dependence of the operator form of the master equation and the decay rates on these correlations as well as on various types of frequency distributions. Furthermore, we use the recently developed bath-positive decomposition method to treat an initially correlated polarization-frequency state of a photon and demonstrate how this allows us to gain new insight and detailed information on how the contributions of different origins influence the photonic dephasing.