Darcie A. Farrow

Polarized pump-probe measurements of electronic motion via a conical intersection.

Polarized femtosecond pump-probe spectroscopy is used to observe electronic wavepacket motion for vibrational wavepackets centered on a conical intersection. After excitation of a doubly degenerate electronic state in a square symmetric silicon naphthalocyanine molecule, electronic motions cause a approximately 100 fs drop in the polarization anisotropy that can be quantitatively predicted from vibrational quantum beat modulations of the pump-probe signal. Vibrational symmetries are determined from the polarization anisotropy of the vibrational quantum beats. The polarization anisotropy of the totally symmetric vibrational quantum beats shows that the electronic wavepackets equilibrate via the conical intersection within approximately 200 fs. The relationship used to predict the initial electronic polarization anisotropy decay from the asymmetric vibrational quantum beat amplitudes indicates that the initial width of the vibrational wavepacket determines the initial speed of electronic wavepacket motion. For chemically reactive conical intersections, which can have 1000 times greater stabilization energies than the one observed here, the same theory predicts electronic equilibration within 2 fs. Such electronic movements would be the fastest known chemical processes.

The polarization anisotropy of vibrational quantum beats in resonant pump-probe experiments: Diagrammatic calculations for square symmetric molecules.

By analogy to the Raman depolarization ratio, vibrational quantum beats in pump-probe experiments depend on the relative pump and probe laser beam polarizations in a way that reflects vibrational symmetry. The polarization signatures differ from those in spontaneous Raman scattering because the order of field-matter interactions is different. Since pump-probe experiments are sensitive to vibrations on excited electronic states, the polarization anisotropy of vibrational quantum beats can also reflect electronic relaxation processes. Diagrammatic treatments, which expand use of the symmetry of the two-photon tensor to treat signal pathways with vibrational and vibronic coherences, are applied to find the polarization anisotropy of vibrational and vibronic quantum beats in pump-probe experiments for different stages of electronic relaxation in square symmetric molecules. Asymmetric vibrational quantum beats can be distinguished from asymmetric vibronic quantum beats by a pi phase jump near the center of the electronic spectrum and their disappearance in the impulsive limit. Beyond identification of vibrational symmetry, the vibrational quantum beat anisotropy can be used to determine if components of a doubly degenerate electronic state are unrelaxed, dephased, population exchanged, or completely equilibrated.

Response functions for dimers and square-symmetric molecules in four-wave-mixing experiments with polarized light

Four-wave-mixing nonlinear-response functions are given for intermolecular and intramolecular vibrations of a perpendicular dimer and intramolecular vibrations of a square-symmetric molecule containing a doubly degenerate state. A two-dimensional particle-in-a-box model is used to approximate the electronic wave functions and obtain harmonic potentials for nuclear motion. Vibronic interactions due to symmetry-lowering distortions along Jahn-Teller active normal modes are discussed. Electronic dephasing due to nuclear motion along both symmetric and asymmetric normal modes is included in these response functions, but population transfer between states is not. As an illustration, these response functions are used to predict the pump-probe polarization anisotropy in the limit of impulsive excitation.

Spectral relaxation in pump–probe transients

The relationship between pump–probe transients and the transition frequency correlation function, M(t), is examined. Calculations of pump–probe transients are carried out with a full-quantum expression for a displaced harmonic oscillator coupled to a heat bath. Pump–probe transients for a slowly decaying, overdamped, Brownian oscillator are shown to resemble a power series in M(t), where the slowest time scale is always equal to the slowest decay in M(t). This equality is consistent with a semiclassical model of pump–probe and valid over the full range of temperature, pulse duration, and detuning explored. The contribution of time scales faster than M(t) to the pump–probe transient increases with increasing temperature, pulse duration, and detuning of the pulse center frequency below resonance. Pump–probe transients for a critically damped oscillator that decays on a femtosecond time scale also have faster early time decay at higher temperatures. Based on these calculations a bootstrap method is suggested for extracting M(t) from pump–probe data starting with the slowest decay. Comparisons are made between simulations of pump–probe and three pulse echo peak shift (3PEPS) transients for a single oscillator and for multiple oscillator systems. Additional fast relaxations similar to those in pump–probe are also present in the 3PEPS transients. For the models investigated, pump–probe is comparable to 3PEPS for the extraction of M(t).

Measurement of Conical Intersection Dynamics by Impulsive Femtosecond Polarization Spectroscopy

The ∼100 fs anisotropy decay from 0.4 toward 0.1 after excitation of a degenerate transition in a square molecule can be predicted from quantum beats of asymmetric vibrations and curve crossing at a conical intersection.