Vibrational echoes: Dephasing, rephasing, and the stability of classical trajectories

The experimental observables in coherent, multiple pulse infrared spectroscopic measurements can be calculated from the nonlinear response functions describing the nuclear dynamics of molecular and condensed phase systems. Within classical mechanics, these nonlinear response functions can be expressed in terms of the monodromy matrices that quantify the stability of classical trajectories. We use an ensemble of noninteracting, anharmonic oscillators to examine the effects of the divergence in time of the classical stability matrix on the analytic properties of the third-order response function, relevant to vibrational echo spectroscopy. The two-pulse echo measurement is designed to rephase a macroscopic variable, that is, to reverse the effects of destructive interference among the dynamics of microscopic systems characterized by a static distribution of energies. Within classical mechanics, this rephasing is shown to preserve the growth with time of the nonlinear response function that is the signature of the divergence of nearby trajectories. For systems with nearly classical nuclear motions, the vibrational echo measurement may then be interpreted as a probe of the stability of atomic trajectories.