Dynamic simulations of hot-electron quantum optics devices

Abstract

It has been a long standing ambition of the mesoscopic community to perform quantum-optics like experiments with electrons. The advent of single photon sources paved new ways of exploring quantum optics phenomena and with the introduction of single electron sources it is hoped that the same advancement within the field of electron quantum optics can be found. Early realisations of these single sources were used for electronic Mach-Zehnder, Hanbury-Brown-Twiss, and Fabry-Perot interferometers. However, they highlight significant difference between electron and photon quantum optics: the quantum statistics of the particles, the presence of the Fermi sea and Coulomb interactions. Recently, experiments using quantum-dot charge pumps have been shown to be a reliable source of single electrons. In addition, they are able to emit electrons at energies far above the Fermi level. These “hot electrons” offer solutions to the previous problems as their energetic separation is thought to isolate them from electron-electron interactions. With the application of a strong magnetic field, edge channels are formed due to the integer quantum Hall effect, which creates ballistic channels for the single electrons mimicking optical paths. The objective of this thesis comprises of two main parts. We begin by creating accurate models of realistic device potentials by introducing a method to model the electrostatic potential at the depth of the two-dimensional electron gas. Previously, other methods which are used to obtain these electrostatic potentials only address the use of one fabrication technique to manipulate the motion of electrons. However, our method incorporates both surface gates of Ti/Au and chemical etching which are used by M. Kataoka at the National Physical Laboratory. We call this the projected surface method which additionally offers a reduction in computational cost over other methods such as the finite element method. The use of this new method is applied to two devices: a time of flight experiment and a Mach-Zehnder interferometer. We will perform analysis on the electrostatic potential acquiring the velocity and spatial trajectory of the electron. The second part of the thesis focuses on the study of the electron transport around these devices using dynamic simulations. By applying a single wave-packet propagation code to their potentials we can model the electrons as Gaussian wave packets and numerically integrate the two-dimensional Schr¨odinger equation to evolve the wave packet around our calculated potentials. This approach utilises the Trotter-Suzuki factorisation and the Fourier split-step method for stability and efficiency. Initially we apply this simulation to simple geometries of devices then continue on to the realistic device potentials, such as the time-of-flight experiment and a variety of quantum point contacts. Not only do the simulations provide detailed time- and energy-resolved information that is accessible experimentally but also provide information about how the electron is travelling within the device between emission and detection.