Monitoring Nonadiabatic Avoided Crossing Dynamics in Molecules by Ultrafast X-Ray Diffraction

We examine time-resolved X-ray diffraction from molecules in the gas phase which undergo nonadiabatic avoided-crossing dynamics involving strongly coupled electrons and nuclei. Several contributions to the signal are identified, representing (in decreasing strength) elastic scattering, contributions of the electronic coherences created by nonadiabatic couplings in the avoided crossing regime, and inelastic scattering. The former probes the charge density and delivers direct information on the evolving molecular geometry. The latter two contributions are weaker and carry spatial information of the transition charge densities (off-diagonal elements of the charge-density operator). Simulations are presented for the nonadiabatic harpooning process in the excited states of sodium fluoride

Utilizing Microcavities to Suppress Third-order Cascades in Fifth-order Raman Spectra

Nonlinear optical signals in the condensed phase are often accompanied by sequences of lower-order processes, known as cascades, which share the same phase matching and power dependence on the incoming fields and are thus hard to distinguish. The suppression of cascading in order to reveal the desired nonlinear signal has been a major challenge in multidimensional Raman spectroscopy, i.e., the $\chi^{(5)}$ signal being masked by cascading signals given by a product of two $\chi^{(3)}$ processes. Since cascading originates from the exchange of a virtual photon between molecules, it can be manipulated by performing the experiment in an optical microcavity. Using a quantum electrodynamical (QED) treatment we demonstrate that the $\chi^{(3)}$ cascading contributions can be greatly suppressed. By optimizing the cavity size and the incoming pulse directions, we show that up to $\sim$99.5\% suppression of the cascading signal is possible.Comment: 15 pages, 2 figures; Accepted by J. Phys. Chem. Let

Detecting Electronic Coherence by Multidimensional Broadband Stimulated X-Ray Raman Signals

Nonstationary molecular states which contain electronic coherences can be impulsively created and manipulated by using recently-developed ultrashort optical and X-ray pulses via photoexcitation, photoionization and Auger processes. We propose several stimulated-Raman detection schemes that can monitor the phase-sensitive electronic and nuclear dynamics. Three detection protocols of an X-ray broadband probe are compared - frequency dispersed transmission, integrated photon number change, and total pulse energy change. In addition each can be either linear or quadratic in the X-ray probe intensity. These various signals offer different gating windows into the molecular response which is described by correlation functions of electronic polarizabilities. Off-resonant and resonant signals are compared

Catching Conical Intersections in the Act; Monitoring Transient Electronic Coherences by Attosecond Stimulated X-Ray Raman Signals

Conical intersections (CoIn) dominate the pathways and outcomes of virtually all photophysical and photochemical molecular processes. Despite extensive experimental and theoretical effort, CoIns have not been directly observed yet and the experimental evidence is being inferred from fast reaction rates and some vibrational signatures. We show that short X-ray (rather than optical) pulses can directly detect the passage through a CoIn with the adequate temporal and spectral sensitivity. The technique is based on a coherent Raman process that employs a composite femtosecond/attosecond X-ray pulse to detect the electronic coherences (rather than populations) that are generated as the system passes through the CoIn

X-Ray sum frequency generation; direct imaging of ultrafast electron dynamics

X-ray diffraction from molecules in the ground state produces an image of their charge density, and time-resolved X-ray diffraction can thus monitor the motion of the nuclei. However, the density change of excited valence electrons upon optical excitation can barely be monitored with regular diffraction techniques due to the overwhelming background contribution of the core electrons. We present a nonlinear X-ray technique made possible by novel free electron laser sources, which provides a spatial electron density image of valence electron excitations. The technique, sum frequency generation carried out with a visible pump and a broadband X-ray diffraction pulse, yields snapshots of the transition charge densities, which represent the electron density variations upon optical excitation. The technique is illustrated by ab initio simulations of transition charge density imaging for the optically induced electronic dynamics in a donor/acceptor substituted stilbene

Monitoring Nonadiabatic Electron-Nuclear Dynamics in Molecules by Attosecond Streaking of Photoelectrons

Streaking of photoelectrons has long been used for the temporal characterization of attosecond extreme ultraviolet pulses. When the time-resolved photoelectrons originate from a coherent superposition of electronic states, they carry an additional phase information, which can be retrieved by the streaking technique. In this contribution we extend the streaking formalism to include coupled electron and nuclear dynamics in molecules as well as initial coherences and demonstrate how it offers a novel tool to monitor non-adiabatic dynamics as it occurs in the vicinity of conical intersections and avoided crossings. Streaking can enhance the time resolution and provide direct signatures of electronic coherences, which affect many primary photochemical and biological events

Non-adiabatic dynamics of molecules in optical cavities

Strong coupling of molecules to the vacuum field of micro cavities can modify the potential energy surfaces opening new photophysical and photochemical reaction pathways. While the influence of laser fields is usually described in terms of classical field, coupling to the vacuum state of a cavity has to be described in terms of dressed photon-matter states (polaritons) which require quantized fields. We present a derivation of the non-adiabatic couplings for single molecules in the strong coupling regime suitable for the calculation of the dressed state dynamics. The formalism allows to use quantities readily accessible from quantum chemistry codes like the adiabatic potential energy surfaces and dipole moments to carry out wave packet simulations in the dressed basis. The implications for photochemistry are demonstrated for a set of model systems representing typical situations found in molecules

Cascading and Local-Field Effects in Non-Linear Optics Revisited; A Quantum-Field Picture Based on Exchange of Photons

The semi-classical theory of radiation-matter coupling misses local-field effects that may alter the pulse time-ordering and cascading that leads to the generation of new signals. These are then introduced macroscopically by solving Maxwell's equations. This procedure is convenient and intuitive but ad hoc. We show that both effects emerge naturally by including coupling to quantum modes of the radiation field in the vacuum state to second order. This approach is systematic and suggests a more general class of corrections that only arise in a QED framework. In the semi-classical theory, which only includes classical field modes, the susceptibility of a collection of $N$ non-interacting molecules is additive and scales as $N$. Second-order coupling to a vacuum mode generates an effective retarded interaction that leads to cascading and local field effects both of which scale as $N^2$