The (Semi-)Classical Vibrational Echo

Abstract

The ultrafast vibrational echo experiment is one of a modern generation of nonlinear coherent optical spectroscopies probing the nuclear dynamics of condensed phases. The vibrational echo is the vibrational analog of the NMR spin echo and selectively eliminates inhomogeneous broadening from the echo spectrum, providing direct information about the timescale of dynamics within a sample. Echo experiments performed by the Fayer group at Stanford University on carbonmonoxy myoglobin discriminate between the dynamic lineshapes of the A states of MbCO. By performing classical molecular dynamics simulations and using nonlinear optical response theory, we have identified the microscopic origins of these states based upon agreement between the experimental vibrational echo decays of the states and echo decays calculated for two distinct structures observed within simulation. We have analysed the properties of the vibrational echo response within the framework of classical mechanics. We have discovered that van Kampen's objection to nonlinear response theory is particularly significant in classical mechanics, where we have shown that the classical echo response function describing the experimental signal diverges in time for a thermal ensemble of noninteracting anharmonic oscillators. We have interpreted the dephasing and rephasing of the vibrational echo experiment in terms of a classical picture which also identifies the classical analogs of quantum mechanical double-sided Feynman diagrams. We have investigated the role of resonant coupling on the quantum mechanical vibrational echo at zero temperature and have analytically taken the classical limit of this expression to investigate the effect of resonance on classical echoes. Finally, we have developed a formalism for utilising the semiclassical Herman-Kluk propagator in the calculation of nonlinear response functions. Applying this formalism we have demonstrated that, for a thermal ensemble of non-interacting Morse oscillators, nearly quantitatively exact approximations to the quantum mechanical vibrational echo signal may be calculated using classical trajectories.