Vibronic Sidebands of Coherent Phonon States

Recently experiments have been reported about phonon sidebands in doped crystals, which may originate from coherent phonon states. The corresponding modes are either confined phonon modes in nanocrystals or localized phonon modes in bulk materials, both showing small damping due to phonon-phonon interaction. We present a theory of the lineshape of vibronic sideband spectra due to coherent phonon states using the conventional model of linear electron-phonon coupling and displaced equilibrium positions of the oscillators in the initial and final electronic states. Unlike in the conventional theory, the initial state of the oscillator is taken as a coherent phonon state and not as a thermalized one. Under these conditions we got an exact analytical solution for the lineshape of the vibronic sideband. The lineshape is determined by two parameters, the Huang-Rhys parameter S and the coherence parameter α of the phonon state. For α = 0 the lineshape converts into the standard Pekarian form for T = 0.