"Exploiting non-Hermiticity in localized plasmonic systems" & "Electron Energy-Gain Spectroscopy: giving a new dimension to nano optics"

Almost a century after the work of Max Planck on the radiation of black bodies, a theoretical proposal of a special type of non-Hermitian Hamiltonians that respect the Parity-Time (PT) symmetry and exhibits real spectra, revived the issue of tackling non-Hermiticity in a meaningful way.1 Despite the distinct physical origins of the Schrödinger equation for electrons and Maxwell theory of photons it can be shown that under certain conditions, they share the similar mathematical structure. One class of non-Hermitian systems consists of open systems that span a wide range of physical situations, from gravity waves close to black holes to lasers cavities or propagating surface plasmons. In those cases, quasi-normal modes (QNMs) are specially constructed so that time-reversal symmetry breaking does not prevent the establishment of a complete basis, especially when PT symmetry is preserved. Another class is represented by localized surface plasmons (LSPs). In this case, the structure of the constituting equation is non-symmetric. In the two cases, a bi-orthogonal rather than orthogonal basis must be used. Bi-orthogonality has a few famous and exciting consequences, including the existence of ‘exceptional points’ where both the energy and wave functions coalesce. Exceptional points are usually associated with the apparition of non-trivial physical effects, such as asymmetric mode switching. Such effects have only very recently been studied experimentally because manipulating QNMs in open systems requires to exactly balance dissipation. In my talk, I will discuss the consequences of bi-orthogonality in localized plasmonic system, the current status of research in this field and my future plans regarding this. 
In the final part of my talk I would like to discuss about electron energy gain spectroscopy. For the last three years, I am developing an instrumental set up for this purpose. As we know, to a first order, in free space, an electron and a photon do not couple, due to the lack of energy-momentum matching. However, the presence of a metal nanostructure or a grating structure can mediate this coupling by supplying the extra momentum. By using synchronized femtosecond pulses of electrons and photons in an electron-microscope set-up, researchers have previously coupled photons to fast electrons through the evanescent light field of a nanostructure. In such cases, electrons could absorb or emit photons many times, resulting in spectra of electron-energy loss (or gain) consisting of a series of peaks evenly spaced according to the energy of the photons.2 The peaks' intensity, and thus the probability of finding an electron in a given state, decreased monotonically with the energy of the electron loss (or gain). Therefore with such a setup one can probe the optical property of materials with high spatial, spectral and temporal resolution in an electron microscope. Another functionality can be added by using a tunable pulsed laser as excitation source. This would enable one to perform electron energy gain spectroscopy by varying the wavelength of the pump laser. This is a new type of spectroscopy named electron energy-gain spectroscopy (EEGS) first theoretically predicted by F. J. García de Abajo and Mathieu Kociak in 2008.3 However, there is no experimental demonstration yet. Combining the spectacular spatial resolution of electron microscopes with the unprecedented spectral resolution of the laser (often few meV) would be a unique tool that does not exist till now and it will enable us to venture into the unchartered domains of nano-optics with high spatial, spectral and temporal resolution. In my talk, I will explain in details the physics, the instrumentation for this purpose, the bottlenecks and show some results towards this direction. I will also explain how this instrumentation can be adapted to any other electron microscope and add extra functionality to probe new Physics.
--------
1 	Bender, C. M., & Boettcher, S. (1998). Real spectra in non-Hermitian Hamiltonians having PT symmetry. Phys. Rev. Lett. 80(24), 5243. 
2 	Barwick, B., Flannigan, D. J., & Zewail, A. H. (2009). Photon-induced near-field electron microscopy. Nature, 462(7275), 902-906. 
3 	de Abajo, F. G., & Kociak, M. (2008). Electron energy-gain spectroscopy. New Journal of Physics, 10(7), 073035.