Nonlinear optical response functions for a chromophore with linear and quadratic electron-vibration coupling

The temperature dependent third-order response function for the Hamiltonian H_e is obtained. In order to demonstrate quantum beats from quadratic coupling, the obtained function is used to calculate the impulsive stimulated photon echo (PE) signal in the limit of large inhomogeneous broadening for a linearly and quadratically coupled phonon. The four-point correlation function defines the echo response functions which enter into the expression for the third-order polarization. Applications are made to impulsive echo spectroscopy. Further, the two-pulse PE signals are calculated in the low temperature limit for the special pair absorption band of the bacterial reaction center and compared with the results of recent accumulated PE experiments.