Two-dimensional spectroscopy for harmonic vibrational modes with nonlinearsystem-bath interactions. II. Gaussian-Markovian case

The relaxation processes in a quantum system nonlinearly coupled to a harmo nic Gaussian-Markovian heat bath are investigated by the quantum Fokker-Pla nck equation in the hierarchy form. This model describes frequency fluctuat ions in the quantum system with an arbitrary correlation time and thus brid ges the gap between the Brownian oscillator model and the stochastic model by Anderson and Kubo. The effects of the finite correlation time and the sy stem-bath coupling strength are studied for a harmonic model system by nume rically integrating the equation of motion. The one-time correlation functi on of the system coordinate, which is measured in conventional Raman and in frared absorption experiments, already reflects the inhomogeneous character of the relaxation process. The finite correlation time of the frequency fl uctuations, however, is directly evident only in the two- and three-time co rrelation function as probed by multidimensional spectroscopic techniques s uch as the Raman echo and the fifth-order 2D Raman experiment.