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The University of Southampton
Mathematical Sciences

Southampton researchers using Nobel prizewinning ideas to study topology of matter

Published: 7 October 2016
Topology of matter

The 2016 Physics Nobel Prize was awarded to the studies of quantum states of matter using mathematical concepts of topology. David Thouless, Duncan Haldane and Michael Kosterlitz showed in the 1970s and 1980s how matter can exist in unusual phases that are "topologically distinct". As an example of topologically distinct objects consider a sphere and a donut. They belong to different classes because continuously deforming a sphere (without tearing its surface) will never change it into a donut, as the latter has a hole in its centre. Similarly, topologically distinct phases of matter are described by mathematical functions which cannot be deformed continuously into each other due to having different topological charges.  This gives rise to dramatically different physical behaviour which can be measured in experiments.

Their work paved the way for modern research on topological matter, such as quantum Hall effect, topological insulators and the ideas of quantum computation where the quantum bits of information are protected by topologically distinct states. One of the most active areas have been synthetic quantum systems that are engineered using ultracold atom clouds, confined in periodic potentials that are formed by interfering laser beams.

The Kosterlitz-Thouless transition was observed in a two-dimensional layer of atoms in Paris in 2006. Also some of the most exotic states that were proposed by Haldane and Thouless were recently experimentally realised by cold-atom research groups in Munich and Zurich.

In Mathematical Sciences at Southampton we are actively studying topologically non-trivial phases in ultracold atom systems, e.g., with some pioneering publications on engineering topological phases of matter for atoms in periodic optical lattices. Here, a tool of choice is the study of the so-called Chern number of the lattice, first applied to these systems by Thouless and collaborators. Using this and other tools, researchers at Southampton have proposed ways to experimentally measure properties of atomic systems, in particular so-called topological bound states which appear at the boundary between two topologically distinct phases of matter.

Current work has also involved experimentalists at the Optoelectronics Research Centre using light in the place of solids as a topological "matter".

 

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