Abstract

Ultrashort, coherent light pulses with wavelengths and durations on the atomic scale are now widely available due to the revolutionary advances made in x-ray free-electron laser (XFEL) technologies in the past few years [1] , [2] . The use of a free-electron gain medium, as opposed to discrete atomic transitions in traditional lasers, provides complete tunability from extreme ultraviolet (100 nm) to hard x-ray (1 Ångstrom) wavelengths – enabling elemental, chemical site and spin selectivity to probe dynamics in complex systems. These ultrashort, tunable x-ray pulses have large energy content (10 12 -10 13 photons/pulse), particularly relative to high harmonic generation (HHG) sources – enabling focused intensities up to 10 20 W/cm 2 and exploration of nonlinear x-ray phenomena [3] - [5] . The transverse coherence of the x-ray pulses generated by self-amplified spontaneous emission (SASE) FELs is excellent [6] – enabling coherent diffraction imaging, x-ray holography and x-ray photon correlation spectroscopy. Going further, a fully coherent FEL pulse with longitudinal coherence is reliably achieved by seeding the source [7] – enabling time-domain coherent control using two phase-coherent waveforms delayed with attosecond precision [8] . The combination of all of these properties from advanced XFELs portend a bright future for multidimensional x-ray spectroscopies to elucidate nuclear and electronic dynamics on the atomic scale that probe not only charge densities and motions, but also quantum coherence and correlations between valence electrons and holes in systems of chemical importance [10] . This tutorial will review XFEL radiation properties and their origins, and illustrate their use via case studies involving molecular dynamics in the gas and liquid phase.

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