Roger Bach

Controlled double-slit electron diffraction

Double-slit diffraction is a corner stone of quantum mechanics. It illustrates key features of quantum mechanics: interference and the particle-wave duality of matter. In 1965, Richard Feynman presented a thought experiment to show these features. Here we demonstrate the full realization of his famous thought experiment. By placing a movable mask in front of a double-slit to control the transmission through the individual slits, probability distributions for single- and double-slit arrangements were observed. Also, by recording single electron detection events diffracting through a double-slit, a diffraction pattern was built up from individual events.

Transverse quantum Stern?Gerlach magnets for electrons

In the Stern–Gerlach experiment, silver atoms were separated according to their spin state (Gerlach and Stern 1922 Z. Phys. 9 353–355). This experiment demonstrates the quantization of spin and relies on the classical description of motion. However, so far, no design has led to a functional Stern–Gerlach magnet for free electrons. Bohr and Pauli showed in the 1930 Solvay conference that Stern–Gerlach magnets for electrons cannot work, at least if the design is based on classical trajectories (Pauli W 1932 Proc. of the 6th Solvay Conf. 2 (1930) (Brussels: Gauthier-Villars) pp 183–86, 217–20, 275–80; Pauli W 1964 Collected Scientific Papers ed R Kronig and V F Weiskopf, vol 2 (New York: Wiley)). Here, we present ideas for the realization of a Stern–Gerlach magnet for electrons in which spin and motion are treated fully quantum mechanically. We show that a magnetic phase grating composed of a regular array of microscopic current loops can separate electron diffraction peaks according to their spin states. The experimental feasibility of a diffractive approach is compared to that of an interferometric approach. We show that an interferometric arrangement with magnetic phase control is the functional equivalent of an electron Stern–Gerlach magnet.

Momentum exchange in the electron double-slit experiment

We provide support for the claim that momentum is conserved for individual events in the electron double slit experiment. The natural consequence is that a physical mechanism is responsible for this momentum exchange, but that even if the fundamental mechanism is known for electron crystal diffraction and the Kapitza-Dirac effect, it is unknown for electron diffraction from nano-fabricated double slits. Work towards a proposed explanation in terms of particle trajectories affected by a vacuum field is discussed. The contentious use of trajectories is discussed within the context of oil droplet analogues of double slit diffraction.

An electron Talbot-Lau interferometer and magnetic field sensing

We present a demonstration of a three grating Talbot-Lau interferometer for electrons. As a proof of principle, the interferometer is used to measure magnetic fields. The device is similar to the classical Moire deflectometer. The possibility to extend this work to build a scaled-up electron deflectometer or interferometer for sensitive magnetic field sensing is discussed.

A wide-angle electron grating bi-prism beam splitter

We demonstrate a wide-angle electron beam splitter capable of producing 1 cm beam separation at the detection plane. The beam splitter utilizes a nanofabricated periodic grating in combination with a bi-prism element. In contrast to devices utilizing only bi-prism elements, the use of the periodic grating causes amplitude, and not wavefront, splitting. Even at maximum separation, beam profiles remain undistorted, providing evidence that coherence is intact. This is a step towards the realization of a large area electron interferometer using such a grating bi-prism combination.

Path integrals, matter waves, and the double slit

Basic explanations of the double slit diffraction phenomenon include a description of waves that emanate from two slits and interfere. The locations of the interference minima and maxima are determined by the phase difference of the waves. An optical wave, which has a wavelength and propagates a distance accumulates a phase of A matter wave, also having wavelength that propagates the same distance accumulates a phase of which is a factor of two different from the optical case. Nevertheless, in most situations, the phase difference, for interfering matter waves that propagate distances that differ by is approximately which is the same value computed in the optical case. The difference between the matter and optical case hinders conceptual explanations of diffraction from two slits based on the matter–optics analogy. In the following article we provide a path integral description for matter waves with a focus on conceptual explanation. A thought experiment is provided to illustrate the validity range of the approximation .