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Chemical Physics

Low-temperature zero phonon lineshapes with various Brownian oscillator spectral densities

Robert S. Knox, Gerald J. Small, Shaul Mukamel

Published Jul 1, 2002• 41 citations
Publisher
DOI
10.1016/s0301-0104(02)00593-1

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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.
We investigate the exact master equation of Hu, Paz, and Zhang for a quantum harmonic oscillator at zero temperature with a Lorentz-Drude type Ohmic spectral density. This master equation plays an important role in the study of quantum Brownian motion and in various applications. In this paper, we give an analytical evaluation of the coefficients of this non-Markovian master equation without Lindblad form, which allows us to investigate consistencies of the solutions, the positivity of the stationary density operator, and the boundaries of the model's parameters.
We investigate the numerical stability of the hierarchical equations of motion (HEOM) method applied to systems with the Brownian oscillator (BO) and multimode BO (MBO) spectral densities. It is shown that, with the increase in the system-bath coupling strength, the standard HEOM may become unstable, and a simple increase in the truncation depth of the HEOM cannot remove the instability at long times. To solve this problem, we first show that the high-temperature approximation of the HEOM with the BO spectral density is equivalent to the celebrated quantum Fokker-Planck equation (QFPE). By starting from the HEOM, we then derive a new multidimensional phase space differential equation that generalizes the QFPE to arbitrary temperature. It is further shown that the numerical instability can be removed if the new low-temperature QFPE is expanded in a basis set different than the one that leads to the conventional HEOM. The matrix product state method is also employed to propagate the new equation based on the low-temperature QFPE and to resolve the numerical instability problem for an electron transfer model with the MBO spectral density presented in the recent literature.