Probing out of-equilibrium optical excitations with fast electrons

Probing optical excitations with nanometer resolution is important for understanding their dynamics and interactions down to the atomic scale. Currently, electron energy-loss spectroscopy (EELS) performed in state-of-the-art... [ view full abstract ]

Probing optical excitations with nanometer resolution is important for understanding their dynamics and interactions down to the atomic scale. Currently, electron energy-loss spectroscopy (EELS) performed in state-of-the-art electron microscopes offers the unparalleled ability of rendering spatially-resolved spectra with combined meV and sub-nm resolution. Additionally, for typical energetic electron beams in the few-to-many keV kinetic energy range, the probability of interaction between a beam electron and an optical excitation is very small, thus preventing modification of the optical response of the sample, unlike other popular techniques based on the used of sharp tips (near-field scanning optical microscopy). A new frontier has recently emerged in this context with the availability of femtosecond electron pulses, which can be synchronized with femtosecond light pulses illuminating the sample. This technique, known as ultrafast electron microscopy, offers the possibility of studying the interaction of beam electrons with highly populated optical modes, which results in multiple energy losses and gains by the electrons, visualized through the recorded electron spectra.

In this theoretical work, we study fundamental aspects of the interaction of fast electrons with localized optical modes. Specifically, we unveil a universal scaling in the interaction strength, depending on the electron energy, the spatial extension of the optical mode, and the optical frequency. We support these findings with extensive numerical simulations for a wide range of morphologies and energies. As an example of potential application, we investigate the differences observed in the electron spectra depending on the statistics of the optical mode (bosons vs fermions) and its population (coherent bosonic states, Fock states, and thermal populations). Based on these results, we propose a new range of experiments intended to probe the quantum characteristics of the sample excitations and their populations.