UC Irvine

Time-resolved, surface-enhanced, coherent anti-Stokes Raman spectroscopy (tr-SECARS) is

ideally suited for preparing and probing vibrational coherences in molecules. By enhancing

the local response of a single molecule with a dipolar nano-antenna, vibrational dynamics

have been measured at the single molecule limit. In contrast with tr-CARS measurements

in ensembles, the vibrational coherence of a single molecule is not subject to pure dephasing.

It exhibits characteristic phase and amplitude noise, which allows the statistical distinction

between single, few, and many molecule sources to be determined. To build on the cur-

rent work, by using three unique pulses to spectrally lter the response of the molecule,

the characteristic noise can be isolated and measured background-free. If the probing of a

superposition state is carried out over a real resonance, then it is possible to tomographically

reconstruct the complete description of quantum dynamics in phase space representation via

the Wigner Distribution Function(WDF). The WDF can be reconstructed from either the

wavepacket via Wigner Transform, or an experimentally measured density, via an Inverse

Radon Transform. The calculations presented here highlight the necessary conditions in

order to reconstruct the WDF with delity from a proposed experiment and compare the

density derived WDF with that of the wavepacket. The principle is rstly demonstrated us-

ing a Kerr gated detection of emission from an evolving state on a bound harmonic potential

energy surface. The model is then explained in the case of a proposed spectrally resolved

transient grating experiment (SRTG). The WDFs generated from the limiting conditions

show that the reproduction delity of the experimentally derived WDF are dependent on

the probe, utilized to measure the evolving superposition, and the curvature, or the vibra-

tional frequency of the potential energy surfaces, and the dephasing time of the vibrational

superposition states. Given two potentials, I show that it is possible to optimize probe

pulse parameters to improve the delity of the state reconstruction. Due to the variational

principle, the negative volume of the WDF, or the Wigner hole, can only be reduced via

measurements - the pulse parameters can be optimized iteratively even when the molecular

potentials are not known.