Non-Ergodic Quantum Manipulation

The subject of electron transport when states are localized by disorder has been an important topic in physics for a considerable time. It was first realized in 2006 that a closed quantum system in which there is both disorder and many body interactions shows a completely new regime of behaviour termed Many Body Localization, MBL. This regime is characterised by a breakdown of equilibrium statistical mechanics, it predicts a zero conductance state at a finite temperature, entanglement can spread although there is a lack of thermalisation due to the breakdown of ergodicity expressed as a violation of the Eigenstate Thermalisation Hypothesis, ETH. Ergodicity is assumed in many areas of condensed matter science, namely that a sub-system of the whole is typical of the whole and that the behaviour averaged over time is identical to that averaged over space. Consequently the fact that it does not hold in this situation allows new phenomena as does the lack of equilibration due to the ETH no longer holding. Possible new states can be formed by the application of high frequencies to MBL and these will be investigated in the project.
To date there has been no sustained experimental investigation of these predictions in condensed matter systems although there is considerable activity using cold atoms which naturally form a closed quantum system. Enormous theoretical interest has been expressed in the hundreds of papers published on the topic.
It is in the area of condensed matter that this new state of matter would have a major impact if realised - which is the purpose of the project. We will comprehensively investigate this regime of behaviour using semiconductor technology and the fabrication techniques used in investigating mesoscopic devices and semiconductor nanostructures.
By fabricating free standing nanostructures we will ensure a closed system by drastically reducing the coupling to the phonons which act as a heat bath. The temperature of measurements will be down the milliKelvin region and the length scale of the disorder will be varied as will other parameters such as dimensionality. Electrical and thermal techniques will be utilised as probes of the MBL state.
In addition to the importance for basic physics this work will be extremely significant in quantum information and topological physics as this new state provides a means of quantum protection not presently available.

The following areas will benefit from the project which has an impact in different fields.
Knowledge
The exploration of non-ergodicity and its consequences in a condensed matter system is a scientific advance on existing knowledge. The breakdown of the Eigenstate Thermalization Hypothesis has not been observed or investigated in condensed matter systems before and is confined to the area of Cold Atoms. This grant combines theory and experiment to make rapid progress which should stimulate other groups both experimental and theoretical to enter this field. As the results will be complementary to the work in Cold Atoms we suggest that a new field of Non-Ergodic Physics will emerge which transcends the division between the atomic work and solid state. The net effect is a rapid increase in knowledge with possible applications in Quantum Technologies.
The fabrication of multi-layer free standing devices and growth techniques for compensated layers all involve advances in techniques which may be of interest to others involved in both physics and material science. As an example, cantilever structures are used as sensitive mass spectrometers and have applications as molecular detectors in the biological/medical area.
Skills
People employed on the project will learn new skills, particularly as they will spend time in each of the collaborating departments, ie low temperature techniques, lithography and semiconductor fabrication. The system we will implement also means that RAs will acquire management and organisational skills, the collaboration with distinguished visitors means that their scientific understanding will increase. The people pipeline will be augmented by our training Ph.D students and offering projects to those in CDTs.
Economy
Success in our project leading to advances in Quantum Technologies will bring a benefit in wealth creation as quantum advances will benefit data processing, security, large data base searching and calculations. These advantages have resulted in the EPSRC quantum initiative. Success in condensed matter physics in the past succeeded in bringing inward investment as Sharp, Hitachi and Toshiba set up laboratories in the UK, one of us, MP, was involved in the Toshiba case. Future success may well bring in more inward investment and our experience will assist in making this a success, we also have experience in making the presentations required. In the consortium we have established 4 companies and have experience in negotiations with venture capital organisations, if the results of the project are sufficiently encouraging we will investigate new company formation. In addition to the benefits of success in quantum information the project may generate spin-off advances in other areas associated with the technology we use, such as spintronics or applications involving thin films, thus there will be advantages to a range of products and procedures.
Society
This project has considerable societal benefits, a major advance in quantum information would benefit healthcare by enhancing more rapid design of new molecules, this would then benefit quality of life. International development will benefit as explained in the letter of support from our collaborator Dr Mark Blumenthal, Lecturer in Physics Capetown University. There are few opportunities for Ph.D students in South Africa to work with physics groups in the developed world, working at the frontiers of physics, and those in Capetown have already benefited from our collaboration and discussions which will be the case in future. Success in a project which is oriented towards basic research, but has benefits in inward investment and new products/technologies, will impact on policy makers and help to convince them to defend the science budget and continue to increase it.