Electron Self-Organisation and Applications

In most situations electrons in semiconductors can be regarded as free with their energy determined by their total number and their effective mass with the mutual repulsion only slightly modifying this free electron picture. However at low values of carrier concentration the repulsion can dominate the manner in which the electrons diffuse in the solid, a voluminous amount of theory has shown that at sufficiently low temperatures the electrons can arrange themselves into a crystalline ensemble. This is termed a Wigner Crystal, or Wigner Lattice, after Wigner who first predicted such a phenomenon, it has proved rather difficult to observe as the observation of a regular structure is not simple and often the predictions of theory are not found due to the presence of disorder.
In one dimension the electrons form a single line and the Wigner Crystal is the trivial case of the electrons seeking a regular periodicity. However, as the confinement weakens, or the electron repulsion increases, so it is possible for the line of electrons to distort as electrons attempt to maximise their separation. In the limit the row splits into two separate rows. The experimental system for such investigations is the electron gas in the GaAs-AlGaAs heterostructure grown by Molecular Beam Epitaxy and the samples are fabricated using high resolution electron beam lithography. In these samples it is possible to control the confinement potential by patterned gates to which voltages are applied, when the samples are sufficiently short electrons drift through ballistically which is without being scattered by random impurities or defects. In this regime the conductance of a one-dimensional wire takes a value 2e2/h where the factor of 2 arises from the spin degeneracy, e is the electron charge and h is Planck's constant. Consequently when a row of electrons splits into 2 rows a conductance of 4e2/h is observed as the ground state. By following the values of conductance as the confinement is changed so the movement of energy levels can be obtained as a function of confinement potential. This has been observed and we call the two rows formed as a result of the electron-electron repulsion the Incipient Wigner Lattice, IWL.
Analysis of the results on the movement of energy levels has shown that prior to the formation of the two separate rows a hybridised state is formed in which two electrons are shared between the two rows such that they form a distorted single row. Quantum Mechanics dictates that two electrons shared in this way must have opposite spins and they can be entangled as a consequence of which they each "know" the quantum state the other is in. Entanglement is a remarkable phenomenon in which if the electrons are separated but still entangled then a change of state of one will produce a change in the state of the other. This remarkable property lies at the heart of many proposals for quantum information processing and quantum logic and may give rise to practical consequences not yet envisaged.
In this research project we propose to study the IWL and optimise the creation of the hybrid state in which the electrons are entangled. Once this state is completely understood the properties of entangled electrons will be studied by injecting them from the IWL into other quantum structures which essentially form an early quantum integrated circuit. One of the characteristics of entangled electrons is that if two of them are in this state then a variation of the wavelength of them is effectively doubled compared to a single electron. Consequently if we perform an interference experiment there is an immediate difference between the behaviour of entangled and normal electrons, this is the effect which we will explore.
The ultimate objective of the work is to develop a method of delivering a stream of entangled electrons and then demonstrate the entanglement in a series of integrated quantum devices with a view to their practical application

The purpose of this work is to explore the physics of electron self-organisation in quasi one-dimensional semiconductor structures when the mutual repulsion of the electrons determines their spatial distribution. Under these circumstances the electrons can entangle, a unique quantum phenomenon in which the electrons form pairs in which each "knows" the quantum state of the other and a change of the state of one will produce a change in the other. This consequence of electron self-organisation gives rise to new quantum phenomena which will be explored, in particular the applications to quantum data processing and computation which has profound consequences for security and rapid assessment of large data bases.
A number of communities will benefit from this work as follows.
The knowledge community will gain considerably from progress in quantum information and spintronics communities as both are seeking new concepts and experimental results. Properties of entangled electrons will be of great interest to the user community of theoretical physicists. The information gained about interfaces and the use of undoped layers will be of significance to Material Scientists and Device Engineers, as the improvements in semiconductor growth can be implemented in the fabrication of high frequency GaAs devices used in mobile phones and other applications. Other communities who will benefit from entanglement based computation include those involved in cryptography, (companies and government establishments), and the medical/biological community who wish to search large data bases and perform parallel computations very quickly, for example crystallographic data bases.
There could be benefit to the economy in that success in the experimental programme described here will stimulate sales of low temperature equipment and associated instrumentation. The growth in the study of two-dimensional systems in recent years has fuelled growth of MBE and processing equipment as well as cryogenic systems, success here would further increase this trend. The longer term development of devices based on the physics explored here could also give rise to sizeable economic benefits.
People will benefit in that there will be considerable advantages to the scientists employed on the grant and Ph.D students who will be associated with it. The science of this work gives rise to new expertise which will be of considerable assistance to Ph.D students and post-doctoral research workers in adjacent areas of physics. This is very important in the context of training given the global competition for skilled personnel and the increasing international competition in new technologies.
There are also benefits to society at large in view of the practical consequence of the quantum physics which is to be investigated. There is considerable interest in sections of the public about the implications of quantum theory such as entanglement, as well as the significance for understanding the meaning of concepts such as superposition of states. The popularity of recent books on these topics indicates the latent interest in the community at large. The generalisation and popularisation of the success of this project will be of considerable interest to this community. Investigators have given general lectures on their research and will continue to seek every opportunity of doing so in the future as part of an outreach policy.
EPSRC has recently identified Quantum Technology including Entanglement and Decoherence as a Grand Challenge, this proposal seeks to address these themes in a new manner.