Design and simulation of a linear electron cavity for quantum electron microscopy

Jaynes-Cummings interaction between low-energy free electrons and cavity photons

The Jaynes-Cummings Hamiltonian is at the core of cavity quantum electrodynamics; however, it relies on bound-electron emitters fundamentally limited by the binding Coulomb potential. In this work, we propose theoretically a new approach to realizing the Jaynes-Cummings model using low-energy free electrons coupled to dielectric microcavities and exemplify several quantum technologies made possible by this approach. Using quantum recoil, a large detuning inhibits the emission of multiple consecutive photons, effectively transforming the free electron into a few-level system coupled to the cavity mode. We show that this approach can be used for generation of single photons, photon pairs, and even a quantum SWAP gate between a photon and a free electron, with unity efficiency and high fidelity. Tunable by their kinetic energy, quantum free electrons are inherently versatile emitters with an engineerable emission wavelength. Hence, they pave the way toward new possibilities for quantum interconnects between photonic platforms at disparate spectral regimes.

Principles of electron wave front modulation with two miniature electron mirrors

We have analyzed the possibilities of wave front shaping with miniature patterned electron mirrors through the WKB approximation. Based on this, we propose a microscopy scheme that uses two miniature electron mirrors on an auxiliary optical axis that is in parallel with the microscope axis. A design for this microscopy scheme is presented for which the two axes can be spatially separated by as little as 1 mm. We first provide a mathematical relationship between the electric potential and the accumulated phase modulation of the reflected electron wave front using the WKB approximation. Next, we derive the electric field in front of the mirror, as a function of a topographic or pixel wise excited mirror pattern. With this, we can relate the effect of a mirror pattern onto the near-field phase, or far field intensity distribution and use this to provide a first optical insight into the functioning of the patterned mirror. The equations can only be applied numerically, for which we provide a description of the relevant numerical methods. Finally, these methods are applied to find mirror patterns for controlled beam diffraction efficiency, beam mode conversion, and an arbitrary phase and amplitude distribution. The successful realization of the proposed methods would enable arbitrary shaping of the wave front without electron-matter interaction, and hence we coin the term virtual phase plate for this design. The design may also enable the experimental realization of a Mach-Zehnder interferometer for electrons, as well as interaction-free measurements of radiation sensitive specimen.

Electrostatic electron mirror in SEM for simultaneous imaging of top and bottom surfaces of a sample

The use of electron mirrors in aberration correction and surface-sensitive microscopy techniques such as low-energy electron microscopy has been established. However, in this work, by implementing an easy to construct, fully electrostatic electron mirror system under a sample in a conventional scanning electron microscope (SEM), we present a new imaging scheme which allows us to form scanned images of the top and bottom surfaces of the sample simultaneously. We believe that this imaging scheme could be of great value to the field of in-situ SEM which has been limited to observation of dynamic changes such as crack propagation and other surface phenomena on one side of samples at a time. We analyze the image properties when using a flat versus a concave electron mirror system and discuss two different regimes of operation. In addition to in-situ SEM, we foresee that our imaging scheme could open up avenues towards spherical aberration correction by the use of electron mirrors in SEMs without the need for complex beam separators.

Flat electron mirror

Electron beams can be reflected by an electrode that is at a more negative potential than the cathode from which the beam is emitted. We want to design a mirror with a flat mirror electrode where the electrons are reflected at a plane very close to the electrode. The wave front of an electron can then be shaped when the mirror contains a surface topography or modulated potential. However, electron beams reflected by flat electron mirrors are usually characterized by high coefficients of chromatic and spherical aberration. When the mirror is combined with an electrostatic lens to form a tetrode mirror system, the situation deteriorates even further. This places a restrictive limit on the maximum aperture angle of the beam, and consequently also limits the attainable resolution at the image plane. We have numerically studied the dependence of these aberrations as a function of design parameters of the tetrode mirror consisting of a ground, lens, cap, and mirror electrode, and limited ourselves to only using flat electrodes with round apertures, at fixed electrode spacing. It turns out that the third order spherical aberration can be made negative. The negative third order aberration is then used to partially compensate the positive fifth order aberration. This way, a system configuration is obtained that, at 2 keV beam energy, provides a diffraction limited resolution of 7.6 nm at an image plane 25 mm from the mirror at beam semi-angles of 2.3 mrad, enabling an illumination radius of 40 μm at the mirror. The presented tetrode mirror design could spark innovative use of patterned electron mirrors as phase plates for electron microscopy in general, and for use as coherent beam splitters in Quantum Electron Microscopy in particular. An appendix presents a method to calculate the spot size of a focused beam in the presence of both third and fifth order spherical aberration coefficients, which is also applicable to Scanning (Transmission) Electron Microscopes with aberration correctors.