Two-dimensional spectroscopy for harmonic vibrational modes with nonlinearsystem-bath interactions. I. Gaussian-white case

The quantum Fokker-Planck equation is derived for a system nonlinearly coup led to a harmonic oscillator bath. The system-bath interaction is assumed t o be linear in the bath coordinates but quadratic in the system coordinate. The relaxation induced dynamics of a harmonic system are investigated by s imulating the higher-order correlation functions of the Raman polarizabilit y and the dipole moment, which represent the nonlinear optical responses of Raman or infrared spectroscopy. The 5th-order Raman response shows that, i n addition to the frequency fluctuations induced by the bath, higher-order energy transfer between the system and bath plays a role. The nonlinearity of the system-bath interaction yields also an interesting feature in the 7t h-order Raman echo or the 3rd-order infrared photon echo response: The calc ulations predict a finite signal for the case of a harmonic potential and a linear coordinate dependence of the polarizability or dipole while for lin ear system-bath coupling this response vanishes completely due to destructi ve interference of different Liouville space pathways.