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arXiv:1506.08226 · Physical Review A

Detecting electronic coherence by multidimensional broadband stimulated x-ray Raman signals

Konstantin E. Dorfman, Kochise Bennett, Shaul Mukamel

Published Aug 17, 2015• 19 citations
arXivHTMLPDF

Abstract

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 subsequent 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.

DOI
10.1103/physreva.92.023826

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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 subsequent 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.
Photoexcited electrons and holes in molecules or in semiconductors constitute a bipartite entangled system. We show that this entanglement can be coherently controlled by broadband x-ray pulses which create valence excitation wave packets through a stimulated Raman process. A novel measure of electron correlations in excited states is then provided by the time dependence of the concurrence. In a simulation study we demonstrate the control of entanglement of electrons and holes in CO that can be achieved by tuning a soft x-ray pulse to different core transitions: the carbon KKK edge (296 eV), the oxygen KKK edge (540 eV), and the $2\ensuremath{\sigma}\ensuremath{\rightarrow}1{\ensuremath{\pi}}^{*}$ transition (191 eV).
Over the past 15 years, researchers have extended the multidimensional techniques which originated with NMR in the 1970s to infrared and visible coherent spectroscopy. These advances have dramatically enhanced the temporal resolution from the microsecond to the femtosecond regime. NMR spectroscopists have developed principles for the design of pulse sequences that enhance selected spectral features and reveal desired dynamical events. Extending these principles to the optical regime offers numerous opportunities for narrowing the line shapes in specific directions, unraveling weak cross-peaks from otherwise congested spectra, and controlling the interferences between quantum pathways. We can achieve these enhancements by shaping the spectral and temporal profiles of the pulses. Pulse polarization shaping may lead to unique probes of time-dependent chirality. In this Account, we compare two types of signals. The first, the photon echo, is generated in the direction -k(1) + k(2) + k(3), and the second, double quantum coherence, is detected at +k(1) + k(2) - k(3). Here k(1), k(2), and k(3) are the wave vectors of the three incoming pulses in chronological order. We illustrate the novel information extracted from these signals by simulations of three physical systems. In the first system, spectra of GaAs semiconductor quantum wells provide a direct look at many-body electron correlation effects. We directly observe specific projections of the many-electron wave function, which we can use to test the quality of various levels of computational techniques for electronic structure. Secondly, the spectra of photosynthetic aggregates reveal couplings between chromophores, quantum coherence signatures of chromophore entanglement, and energy-transfer pathways. Using some fundamental symmetries of pulse polarization configurations of nonlinear signals, we can construct superpositions of signals designed to better distinguish among various coherent and incoherent exciton transport pathways and amplify subtle variations among different species of the Fenna-Matthews-Olson (FMO) antenna complex. Both of the first two applications require femtosecond pulses of light in the visible range. The third application demonstrates how resonant core spectroscopy may be used to generate core excitations that are highly localized at selected atoms. Such signals can monitor the motions of valence electron wavepackets in real space with atomic spatial resolution. These future X-ray applications will require attosecond bright X-ray sources, which are currently being developed in several labs. Common principles underlie these techniques in coherent spectroscopy for spins, valence electrons, and core electronic excitations, spanning frequencies from radiowaves to hard X-rays.
The temporal dynamics of stimulated emission is studied, with particular emphasis on stimulated emission induced by x-ray pulses interacting with nuclei. In typical nuclear forward scattering experiments, the short incident x-ray pulse is accompanied by a huge number of off-resonant background photons. This prompts the question of whether stimulated emission can be observed in the delayed nuclear scattering signal which is emitted after the incident pulse has passed. We find that the stimulated photons essentially overlap with the stimulating pulse. To overcome this problem, we identify the reduction of the delayed scattered light intensity as an alternative signature for the stimulated emission. We further study a phase-sensitive variant of stimulated emission in the low-excitation regime, which provides convenient control parameters to facilitate the detection. Finally, we analyze the possibility of observing stimulated emission in nuclei driven by free electron lasers or synchrotron radiation sources.
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We propose an approach to probe coherent spin-state dynamics of molecules using circularly polarized hard X-ray pulses. For the dynamically aligned nitric oxide molecules in a coherent superposition spin-orbit coupled electronic state that can be prepared through stimulated Raman scattering, we demonstrate the capability of ultrafast X-ray diffraction to not only reveal the quantum beating of the coherent spin-state wave packet but also image the spatial spin density of the molecule. With a circularly polarized ultrafast X-ray diffraction signal, we show that the electronic density matrix can be retrieved. The spatiotemporal resolving power of ultrafast X-ray diffraction paves the way for tracking transient spatial wave function in molecular dynamics involving the spin degree of freedom.