Electron-Enabled Nanoparticle Diffraction

Abstract

Matter-wave interferometry is a phenomenon which has been utilized and studied in electron microscopy since the early days of electron optics, with the development of phase contrast imaging, electron diffraction, electron holography, etc. When an electron diffracts off of a crystal lattice, it enters a superposition state of eligible Bragg diffraction components; due to momentum conservation, the crystalline sample must receive an equal and opposite superposition of momentum transfers. In theory, this results in an entangled electron-sample state. Typically, however, the sample is extremely large relative to the electron and is held fast in a sample holder, and this reciprocal momentum transfer is unobservable [1]. We present a proposal [2] to establish a system where such momentum kicks would be resolvable, to enable probing of the matter-wave properties of the sample as well as the free electron. A crystalline silicon nanoparticle is levitated in the sample plane, then released from its trap to enter free-fall. A single electron impacts the nanoparticle and undergoes Bragg diffraction. The nanoparticle receives a momentum transfer from the diffraction and is allowed to continue free-falling for a fixed amount of time before recapture and measurement of its position, X. In synchrony, the position of the electron, x, is measured. Assuming perfect measurement resolution, we calculate the resulting interference pattern for a quantum interaction, where the nanoparticle can behave as a quantum wave (Fig. 1a), or for the case where it behaves as a classical grating aperture (Fig. 1b) for different recapture times, t. The quantum scenario presents additional fringes visible at specific recapture times. Such an experiment provides a test of the matter-wave behaviour of high mass nanoparticles, with an efficient duty cycle and a short interference time, and would allow access to electron-sample entanglement in a transmission electron microscope.