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Tracking the motion of charges in a terahertz light field by femtosecond X-ray diffraction


In condensed matter, light propagation near resonances is described in terms of polaritons, electro-mechanical excitations in which the time-dependent electric field is coupled to the oscillation of charged masses1,2. This description underpins our understanding of the macroscopic optical properties of solids, liquids and plasmas, as well as of their dispersion with frequency. In ferroelectric materials, terahertz radiation propagates by driving infrared-active lattice vibrations, resulting in phonon-polariton waves. Electro-optic sampling with femtosecond optical pulses3,4,5 can measure the time-dependent electrical polarization, providing a phase-sensitive analogue to optical Raman scattering6,7. Here we use femtosecond time-resolved X-ray diffraction8,9,10, a phase-sensitive analogue to inelastic X-ray scattering11,12,13, to measure the corresponding displacements of ions in ferroelectric lithium tantalate, LiTaO3. Amplitude and phase of all degrees of freedom in a light field are thus directly measured in the time domain. Notably, extension of other X-ray techniques to the femtosecond timescale (for example, magnetic or anomalous scattering) would allow for studies in complex systems, where electric fields couple to multiple degrees of freedom14.

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Figure 1: Excitation of phonon polaritons in LiTaO3.
Figure 2: Optical pump, X-ray diffraction probe experimental apparatus.
Figure 3: Measurement of the time-dependent change in the 006 diffracted intensity.


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We thank M. Khalil for her help during data acquisition. We are grateful to J. S. Wark for discussions, as well as for sharing the results of dynamic diffraction simulations for LiTaO3. We thank K. Sokolowski-Tinten, R. Merlin, D. Reis and S. Hooker for many discussions, suggestions and for critical reading of our manuscript. Help by N. Tamura with the measurement of static Laue patterns in LiTaO3 is also gratefully acknowledged. Experiments at LBNL were supported by the Director, Office of Science, Office of Basic Energy Sciences, Division of Materials Science and Engineering Division, of the US Department of Energy. Work at the University of Oxford was supported by the European Science Foundation through a European Young Investigator Award. S.W. acknowledges receipt of a graduate scholarship from the UK Engineering and Physical Sciences Research Council. Simulation work at MIT was funded by the US National Science Foundation.

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Cavalleri, A., Wall, S., Simpson, C. et al. Tracking the motion of charges in a terahertz light field by femtosecond X-ray diffraction. Nature 442, 664–666 (2006).

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