RESUMO
Holography relies on the interference between a known reference and a signal of interest to reconstruct both the amplitude and the phase of that signal. With electrons, the extension of holography to the ultrafast time domain remains a challenge, although it would yield the highest possible combined spatiotemporal resolution. Here, we show that holograms of local electromagnetic fields can be obtained with combined attosecond/nanometer resolution in an ultrafast transmission electron microscope (UEM). Unlike conventional holography, where signal and reference are spatially separated and then recombined to interfere, our method relies on electromagnetic fields to split an electron wave function in a quantum coherent superposition of different energy states. In the image plane, spatial modulation of the electron energy distribution reflects the phase relation between reference and signal fields. Beyond imaging applications, this approach allows implementing quantum measurements in parallel, providing an efficient and versatile tool for electron quantum optics.
RESUMO
Surface plasmon polaritons can confine electromagnetic fields in subwavelength spaces and are of interest for photonics, optical data storage devices and biosensing applications. In analogy to photons, they exhibit wave-particle duality, whose different aspects have recently been observed in separate tailored experiments. Here we demonstrate the ability of ultrafast transmission electron microscopy to simultaneously image both the spatial interference and the quantization of such confined plasmonic fields. Our experiments are accomplished by spatiotemporally overlapping electron and light pulses on a single nanowire suspended on a graphene film. The resulting energy exchange between single electrons and the quanta of the photoinduced near-field is imaged synchronously with its spatial interference pattern. This methodology enables the control and visualization of plasmonic fields at the nanoscale, providing a promising tool for understanding the fundamental properties of confined electromagnetic fields and the development of advanced photonic circuits.
RESUMO
The experimental temperature dependence (T = 2-300 K) of single crystal bulk and site susceptibilities of rare earth titanate pyrochlores R(2)Ti(2)O(7) (R = Sm, Eu, Gd, Tb, Dy, Ho, Er, Yb) is analyzed in the framework of crystal field theory and a mean field approximation. Analytical expressions for the site and bulk susceptibilities of the pyrochlore lattice are derived taking into account long range dipole-dipole interactions and anisotropic exchange interactions between the nearest neighbor rare earth ions. The sets of crystal field parameters and anisotropic exchange coupling constants have been determined and their variations along the lanthanide series are discussed.
