Title:

Electron dynamics in surface acoustic wave devices

Gallium arsenide is piezoelectric, so it is possible to generate coupled mechanical and electrical surface acoustic waves (SAWs) by applying a highfrequency voltage to a transducer on the surface of GaAs. By combining SAWs with existing lowdimensional nanostructures one can create a series of dynamic quantum dots corresponding to the minima of the travelling electric wave, and each dot carries a single electron at the SAW velocity (~ 2800 m/s). These devices may be of use in developing future quantum information processors, and also offer an ideal environment for probing the quantum mechanical behaviour of single electrons. This thesis describes a numerical and theoretical study of the dynamics ofan electron in a range of geometries. The numerical techniques for solving thetimedependent Schrödinger equation with an arbitrary timedependent potential will be described in Chapter 2, and then applied in Chapter 3 to calculate the transmission of an electron through an AharonovBohm (AB) ring. It will be seen that an important property of the techniques used in this thesis is that they can be easily adapted to study realistic geometries, and we will see features in the AB oscillations which do not arise in simplified analytic descriptions. In Chapter 4, we will then study a device consisting of two parallel SAW channels separated by a controllable tunnelling barrier. We will use numerical simulations to investigate the effect of electric and magnetic fields upon the electron dynamics, and develop an analytic model to explain the simulation results. From the model, it will be apparent that it is possible to use this device to rotatethe state of the electron to an arbitrary superposition of the first two eigenstates. We then introduce coherent and squeezed states in Chapter 5, which are excited states of the quantum harmonic oscillator. Coherent and squeezed electronicstates may be of use in quantum information processing, and could also arise dueto unwanted perturbations in a SAW device. We will discuss how these statescan be controllably generated in a SAW device, and also discuss how they couldthen be detected. In Chapter 6 we describe how to use the motion of a SAW to create a rapidlychanging potential in the frame of the electron, leading to a nonadiabatic excitation. The nonadiabaticallyexcited state oscillates from side to side within a 1Dchannel on a fewpicosecond timescale, and this motion can be probed by placing a tunnelling barrier at one side of the channel. Numerical simulations will beperformed to show how this motion can be controlled, and the simulation resultswill be seen to be in good agreement with recent experimental work performed by colleagues. Finally, we will show that this device can be used to measure the initial state of an electron which is an arbitrary superposition of the first twoeigenstates.
