Application of density matrix Wigner transforms for ultrafast macromolecular and chemical x-ray crystallography.

Time-Resolved Serial Femtosecond Crystallography (TR-SFX) conducted at X-ray Free Electron Lasers (XFELs) has become a powerful tool for capturing macromolecular structural movies of light-initiated processes. As the capabilities of XFELs advance, we anticipate that a new range of coherent control and structural Raman measurements will become achievable. Shorter optical and x-ray pulse durations and increasingly more exotic pulse regimes are becoming available at free electron lasers. Moreover, with high repetition enabled by the superconducting technology of European XFEL (EuXFEL) and Linac Coherent Light Source (LCLS-II) , it will be possible to improve the signal-to-noise ratio of the light-induced differences, allowing for the observation of vibronic motion on the sub-Angstrom level. To predict and assign this coherent motion, which is measurable with a structural technique, new theoretical approaches must be developed. In this paper, we present a theoretical density matrix approach to model the various population and coherent dynamics of a system, which considers molecular system parameters and excitation conditions. We emphasize the use of the Wigner transform of the time-dependent density matrix, which provides a phase space representation that can be directly compared to the experimental positional displacements measured in a TR-SFX experiment. Here, we extend the results from simple models to include more realistic schemes that include large relaxation terms. We explore a variety of pulse schemes using multiple model systems using realistic parameters. An open-source software package is provided to perform the density matrix simulation and Wigner transformations. The open-source software allows us to define any arbitrary level schemes as well as any arbitrary electric field in the interaction Hamiltonian.

Optical control of ultrafast structural dynamics in a fluorescent protein.

The photoisomerization reaction of a fluorescent protein chromophore occurs on the ultrafast timescale. The structural dynamics that result from femtosecond optical excitation have contributions from vibrational and electronic processes and from reaction dynamics that involve the crossing through a conical intersection. The creation and progression of the ultrafast structural dynamics strongly depends on optical and molecular parameters. When using X-ray crystallography as a probe of ultrafast dynamics, the origin of the observed nuclear motions is not known. Now, high-resolution pump-probe X-ray crystallography reveals complex sub-ångström, ultrafast motions and hydrogen-bonding rearrangements in the active site of a fluorescent protein. However, we demonstrate that the measured motions are not part of the photoisomerization reaction but instead arise from impulsively driven coherent vibrational processes in the electronic ground state. A coherent-control experiment using a two-colour and two-pulse optical excitation strongly amplifies the X-ray crystallographic difference density, while it fully depletes the photoisomerization process. A coherent control mechanism was tested and confirmed the wave packets assignment.