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Signatures of quantum coherence in the optical line shape of an exciton in the presence of dynamic disorder

We address the effects of quantum coherences on the optical line shape of an exciton in the presence of dynamic disorder. We consider a one-dimensional excitonic system that consists of two levels placed at regular intervals. Detailed analytical calculations of line shape have been carried out by using Kubo's stochastic Liouville equation (K-QSLE). We make use of the observation that in the site representation, the Hamiltonian of our system with constant off-diagonal coupling J is a tridiagonal Toeplitz matrix (TDTM) whose eigenvalues and eigen functions are known analytically. This identification is particularly useful for long chains where the eigen values of TDTM help to understand crossover between static and fast modulation limits. We summarize the new results as follows. (i) In the slow modulation limit when the bath correlation time is large, the effects of spatial correlation are not negligible. Here the line shape is broadened and the number of peak increases beyond the ones obtained from TDTM (constant off-diagonal coupling element J and no fluctuation). (ii) However, in the fast modulation limit when the bath correlation time is small, the spatial correlation is less important (iii) Importantly, we find that the line shape can capture that quantum coherence affects in the two limits differently.