Two-dimensional spectroscopy for a two-dimensional rotator coupled to a Gaussian–Markovian noise bath

The dynamics of a system in the condensed phase are more clearly characterized by multitime correlation functions of physical observables than by two-time ones. We investigate a two-dimensional motion of a rigid rotator coupled to a Gaussian–Markovian harmonic oscillator bath to probe this issue. The analytical expression of a four-time correlation function of a dipole that is the observable of two-dimensional microwave or far-infrared spectroscopy is obtained from a generating functional approach. The spectra in the absence of damping are discrete and reveal transitions between eigenstates of the angular momentum quantized due to the cyclic boundary condition. For a weakly damped case, the two-dimensional spectrum predicts three echolike peaks corresponding to transition processes between the rotational energy levels, which cannot be observed in one-dimensional (linear-absorption) spectroscopy related to the two-time correlation function of the dipole [J. Phys. Soc. Jpn. 71, 2414 (2002)]. The two-dimensional spectra are more sensitive to the noise effects than the one-dimensional spectra. It is because the effects of the initial thermal distribution determine the profile of the continuous line shape in one-dimensional spectroscopy, while such thermal effects are canceled through the higher-order optical transition process in two-dimensional spectroscopy. If the rotator system is strongly coupled to the colored noise bath, the system exhibits one overdamped and other oscillatory motions. We observe peaks arising from interaction between these two modes in the two-dimensional spectra, which are difficult to distinguish in one-dimensional spectra.