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We investigate excitonic polaron states comprising a local exciton andphonons in the longitudinal optical (LO) mode by solving the Schr\"{o}dingerequation. We derive an exact expression for the ground state (GS), whichincludes multi-phonon components with coefficients satisfying the Huang-Rhysfactors. The recombination of GS and excited polaron states gives one set ofsidebands in photoluminescence (PL): the multi-phonon components in the GSproduce the Stokes lines and the zero-phonon components in the excited statesproduce the anti-Stokes lines. By introducing the mixing of the LO mode andenvironal phonon modes, the exciton will also couple with the latter, and theresultant polaron states result in another set of phonon sidebands. This sethas a zero-phonon line higher and wider than that of the first set due to thetremendous number of the environal modes. The energy spacing between thezero-phonon lines of the first and second sets is proved to be the bindingenergy of the GS state. The common exciton origin of these two sets can befurther verified by a characteristic Fano lineshape induced by the coherence inthe mixing of the LO and the environal modes.Comment: 5 pages, 3 figures 1 figure (fig. 1) replaced 1 figure (fig. 2)  remove

Phonon coherence and new set of sidebands in phonon-assisted photoluminescence