Disorder influenced absorption line shapes of a chromophore coupled to two-level systems

We have carried out a theoretical and numerical study of disorder-induced changes in the absorption line shape of a chromophore embedded in a host matrix. The stochastic sudden jump model is employed wherein the host matrix molecules are treated as noninteracting two-level systems (TLSs) occupying points on a three-dimensional lattice with randomly oriented dipole moments. By systematically controlling the degree of positional disorder (α) attributed to them, a perfectly crystalline (α = 0) or a glassy environment (α = 1) or a combination of the two is obtained. The interaction between the chromophore and the TLSs is assumed to be of the dipole-dipole form. With an increase in α, the broadening of the absorption line shape was found to follow a power-law behavior. More importantly, it is revealed in the long-time limit that the resultant line shape is Gaussian in the absence of disorder but transforms to Lorentzian for a completely disordered environment. For an arbitrarily intermediate value of α, the resultant line shape can be approximately fitted by a linear combination of Gaussian and Lorentzian components. The Lorentzian profile for the disordered medium is attributed to the chomophore-TLS pairs with vanishingly small separation between them.