Spectroscopy of a chromophore coupled to a lattice of dynamic twohyphen;level systems. II. Spectral diffusion kernel

摘要

We consider the spectral diffusion of a chromophore coupled through dipolar interactions to a regular lattice of flipping twohyphen;level systems. In particular, we calculate the spectral diffusion kernel,P(ohgr;,tVerbar;ohgr;0), which is the conditional probability density that the chromophore will have transition frequency ohgr; at timet, given that it had frequency ohgr;0at time 0. At very short times we find that the spectral diffusion kernel is Lorentzian, for any value of the twohyphen;level system excitation probability,p. For longer times the form of the spectral diffusion kernel depends on the value ofp. We derive several approximate expressions for the spectral diffusion kernel, all of which go to the correct equilibrium distribution of frequencies for long times. Forpbartil;1/2, when the frequency distribution is nearly Gaussian, we find that the spectral diffusion kernel is not at all Gaussian for short times. We compare all of our approximate expressions with numerically exact results. Motivated by certain optical spectral diffusion experiments on individual molecules in solids, we also calculateP(Dgr;;t), the distribution of spectral jumps, which is the probability density that the chromophorersquo;s frequency will change by an amount Dgr; in timet. In a subsequent paper we will analyze these spectral diffusion experiments with our results.