Modeling of fluence-dependent hole-burned spectra and hole-growth kinetics using multiple two-level system model

Numerical formalism is presented that perfectly describes resonant low-temperature hole-burned spectra (including zero-phonon holes, ZPHs) and spectral hole-growth dynamics of Al-phthalocyanine tetrasulphonate embedded in hyperquenched glassy water films over more than seven orders of fluence magnitude (0.4 µJ/cm2-5.9 J/cm2). Frequency changes during spectral hole-burning (HB) are traditionally explained with the help of a single extrinsic two-level-system (TLSext) associated with impurity molecules. The new multiple two-level system (n-TLSext) models and data analysis presented in this work show that each chromophore in an amorphous medium can couple with multiple independent TLSext, which maintain perfect photo-memory, allowing a full return of the photoproduct to the initial ("preburn") state. Modeling reveals that the experimentally observed narrow photoproduct peak at higher energies, in close vicinity of the zero-phonon hole (ZPH), reflects a dynamical feature of the HB process populating so-called "terminal" states (states that do not interact with laser excitation). Within the n-TLSext model, each chromophore possesses multiple possibilities to create a photoproduct when in interaction with the burning laser, i.e., chromophores can interact with burning laser-light multiple times until reaching the terminal states. Due to phonon-assisted absorption, terminal states are typically at higher energies than the ZPH, in agreement with the hole burned spectra reported for many molecules embedded in various amorphous solids. However, many HB systems reveal both blue- (high-energy) and red-shifted (low-energy) antiholes (i.e., photoproducts). We suggest that future modeling of resonant holes in various proteins using our n-TLSext model will provide more insight on the complexity of the protein energy landscape.