The millivolt energy resolution now obtainable in electron energy-loss spectra (EELS) on the latest monochromated scanning transmission electron microscope corresponds, via the uncertainty principle, to a time range of 414 fs (for 10 meV resolution), and a time resolution of 0.138 fs (for energy range of 30 eV). (Thus, the width of an EELS peak is inversely related to the lifetime of an excitation.) This compares favorably with the latest X-ray free electron lasers. The time evolution of a Drude–Lorentz oscillator may be obtained from an EELS using logarithmic deconvolution followed by Kramers–Kronig analysis to extract the frequency-dependent dielectric function, and a final Fourier transform from frequency to time domain. This time-dependent dielectric function was interpreted as the impulse response of electrons, phonons, or ions based on the Drude–Lorentz theory. The time evolution of electronic oscillators from ice and protein, extracted from low resolution experimental data, were compared. Using higher energy resolution data we have also extracted the time-resolved spectra from excitons in an alkali halide, BaF2. Despite the small scanning transmission electron microscope probe size, delocalization limits the spatial resolution to about 50 nm, which is, nevertheless, better than the millimeter resolution of infrared absorption spectroscopy or Raman spectroscopy.
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