Back to search

FRINATEK-Fri prosj.st. mat.,naturv.,tek

TOPOLOGICAL QUANTUM PHENOMENA IN LOW DIMENSIONAL SYSTEMS

Awarded: NOK 1.2 mill.

Project Number:

213606

Application Type:

Project Period:

2012 - 2017

Location:

Ever since the theoretical prediction by Leinaas and Myrheim in 1979 of anyons [a new type of quantum particles that can exist only in two dimensions - as opposed to our usual, three-dimensional world], it has been known that number of "exotic" quantum phenomena are permitted if the theory is restricted to lower, i.e. two or one, dimensions. Some of these ideas became experimentally manifest as the quantum Hall effect was discovered a few years later. Since then the field has developed enormously. The quantum Hall effect is in a sense the prototype of what is now called "topological phases", which are being looked for in a number of materials. One of the main motivations is the prospect to generate and control the anyons that are expected to exist in these materials -- with the long term goal of creating a particularly robust type of quantum computer. In fact, Microsoft has invested substantially in funding basic research in this area. The present FRIPRO project addresses theoretically a number of aspects of such topological phenomena. For example, we study the properties of anyonic quasiparticles in one-dimensional quantum wires and in the quantum Hall effect, the possibility of realizing similar physics in the context of atomic Bose condensates, as well as quantum magnetism in low-dimensional materials. Some highlights of results so far: * The planned review article on quantum Hall hierarchies (about 60 pages) has been finalized and will shortly appear in the very prestigious journal Reviews of Modern Physics * During the study of quantum mechanical wave functions describing rotating two-species Bose condensates in the lowest Landau level, some surprising mathematical features of these wave functions were discovered. These have been studied and understood in detail. (2 papers, 3rd manuscript in progress) * Magnetic Bloch oscillations are a (theoretically predicted) purely quantum mechanical effect that has so far not been observed. Numerical modeling has led us to propose concrete experimental conditions under which this effect may be observed in neutron scattering experiments. * One day some exotic superconductors might be used to realise a quantum computer. However, these superconductors require extremely low temperatures. We have shown how these superconductors can be made more robust by coupling them to a conventional high temperature superconductor. * We have studied the special properties of charged excitations on the edge of the quantum Hall system, which are different from excitations in the bulk. In particular we have now found out how their quantum statistics varies continuously as one varies the interaction between the two edges. The aim is to get a more complete picture of the interesting quantum Hall "edge physics", which is also relevant to experiments.

This is a project of basic research in theoretical physics, where our goal is to deepen and extend the understanding of fundamental quantum phenomena in low dimensional systems. In later years there has been an increasing interest in the study of quantu m systems confined to one and two dimensions. This field has attracted prominent theoretical physicists as well as experimentalists world wide. The attraction is due to developments in the field, which show that new and interesting phenomena may arise whe n the dimension is reduced. Especially we will study various aspects of what happens when "standard" theory of condensed matter systems breaks down in low dimensional systems. That is when quantum fluctuations are large or the many-body aspects become overwhelming. Unconventional states of matter that do not follow the "standard" rules of condensed matter physics do exist, and recently it has been proposed that topology can play a role to describe ground states and excitations of some of these. This is an exciting direction which will pursued in parts of this project. The discoveries of unconventional states of matter have mostly come as experimental surprises, and there are probably more surprises to come. A part of the usefulness of this projec t is to extend and deepen our theories of interacting particles in low dimensional systems in order to explain and utilize such future discoveries. Moreover a solid theoretical understanding of the physics of these systems is a crucial prerequisite for fu ture technological applications.

Publications from Cristin

No publications found

Funding scheme:

FRINATEK-Fri prosj.st. mat.,naturv.,tek