Coherent-phonon vibronic sideband

We present the theory of vibronic sideband spectra due to coherent phonon modes using the conventional model of linear electron-phonon coupling and displaced equilibrium positions of the oscillators in the exited 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 sideband 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