Spectroscopy of a chromophore coupled to a lattice of dynamic two-level systems. I. Absorption line shape

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Abstract
Frequency modulation of a dilute chromophore’s transition is a common mechanism of line broadening in condensed phases. In many different physical situations this frequency modulation arises from coupling of the chromophore to a collection of flipping two-level systems. In this paper we calculate the absorption line shape for such a chromophore when the two-level systems occupy the sites of a regular lattice. We consider both general and specific (dipolar) two-level system/chromophore interactions. We present both exact (numerical) and approximate (analytical) expressions for the line shape as a function of the two-level system excitation probability, p, and the flip rate. We find that when p≪1 the line shape is Lorentzian for any value of the flip rate, and that when p=1/2 the chromophore’s fluctuating frequency is described approximately by a Gaussian random process, and that therefore the seminal stochastic model of Anderson and Kubo is applicable.