Ohmic Brownian oscillator approach to hole-burning and photon-echo spectroscopies

The multimode Brownian oscillator (MBO) model has been at the forefront in interpreting the subsystem-bath interaction manifestations in optical spectroscopy for probing homogeneous structure of chromophores in crystals and amorphous solids. The spectroscopic consequences of employing the underdamped MBO model with Ohmic dissipation in linear absorption, photon-echo, and hole-burning data of chromophores in solid hosts at low temperatures are investigated. The zero-phonon line (ZPL) in homogeneous linear absorption spectrum, the slow-decay component (due to ZPL) in photon-echo signal, and the zero-phonon hole (ZPH) in hole-burned spectra in host molecular solids at low temperatures are usually resolved from the multiphonon-transitions structure. In the MBO model, the harmonic vibrations (Brownian oscillators) are linearly coupled to bath modes. This coupling, with Ohmic dissipation, results in a maximum contribution of the bath modes to the ZPL region. This contribution affects the width of the ZPL profile, which should only be determined by pure electronic dephasing as dictated by experiments. It is therefore important to study how the MBO model bath modes contribute to the ZPL, ZPH, and slow-decay component profiles. Analytical expressions for the linear absorption spectrum and width and Franck-Condon factor of the ZPL are derived. Homogeneous linear absorption spectra, two-pulse photon-echo, and hole-burning calculations are carried out with model systems of which the parameter values are typical for real systems, The MBO model ZPL, ZPH, and slow-decay component were not seen in linear absorption, hole-burning, and two-pulse photon-echo profiles, respectively. The hole-burned spectrum is produced by blending the line broadening function, g(t;T), of the MBO model and Small hole-burning formula. This full (inclusion of Matsubara series) form of g(t;T) has not been exploited before in any spectroscopic calculation. It is concluded that the MBO model ZPL and ZPH widths and the electronic exponential decay are better exhibited in the corresponding profiles when using non-Ohmic spectral density.