A Laboratory Frame Density Matrix for Ultrafast Quantum Molecular Dynamics

TL;DR

This paper introduces a formalism connecting molecular and laboratory frame quantum dynamics, enabling better interpretation of ultrafast molecular experiments and defining methods for molecular frame quantum tomography.

Contribution

It provides a lab frame density matrix formalism that links molecular dynamics to experimental measurements and introduces Molecular Angular Distribution Moments for improved data representation.

Findings

Reveals orientation dependence of molecular dynamics in experiments

Defines a molecular frame quantum tomography procedure

Identifies limitations of orientation-averaged density matrices

Abstract

In most cases the ultrafast dynamics of resonantly excited molecules are considered, and almost always computed in the molecular frame, while experiments are carried out in the laboratory frame. Here we provide a formalism in terms of a lab frame density matrix which connects quantum dynamics in the molecular frame to those in the laboratory frame, providing a transparent link between computation and measurement. The formalism reveals that in any such experiment, the molecular frame dynamics vary for molecules in different orientations and that certain coherences which are potentially experimentally accessible are rejected by the orientation-averaged reduced vibronic density matrix. Instead, Molecular Angular Distribution Moments (MADMs) are introduced as a more accurate representation of experimentally accessible information. Furthermore, the formalism provides a clear definition of a molecular frame quantum tomography, and specifies the requirements to perform such a measurement enabling the experimental imaging of molecular frame vibronic dynamics. Successful completion of such a measurement fully characterizes the molecular frame quantum dynamics for a molecule at any orientation in the laboratory frame.