Forum for Science, Industry and Business

Sponsored by:     3M 
Search our Site:

 

A new simulatable model displaying exotic quantum phenomena

28.11.2013
Scientists at MPQ develop a new model for realizing the Fractional Quantum Hall Effect in lattice systems

It is fascinating how quantum mechanical behaviour of particles at smallest scales can give rise to strange properties that can be observed in the classical world. One example is the Fractional Quantum Hall Effect (FQH) that was discovered about 30 years ago in semiconductor devices.


Fig. 1

It is one of the most striking phenomena in condensed matter physics and has been thoroughly investigated. Nowadays experimental physicists are able to model effects occurring in condensed matter with ultracold atoms in optical lattices. This has sparked the interest in the question under which conditions the FQH could be observed in such systems.

Now Anne Nielsen and co-workers from the Theory Division of Professor Ignacio Cirac at the Max-Planck-Institute of Quantum Optics and at the Universidad Autónoma de Madrid have developed a new lattice model which gives rise to FQH-like behaviour (Nature Communications, 28 November 2013).

The classical Hall-effect describes the behaviour of electrons or, generally spoken, charge carriers in an electrical conducting probe under the influence of a magnetic field that is directed perpendicular to the electric current. Due to the Lorentz-force a so-called Hall-voltage builds up, which increases linearly with the magnetic field.

In 1980 the German physicist Klaus von Klitzing investigated the electronic structure of so-called MOSFETs. At extremely low temperatures and extremely high magnetic fields he made the discovery that the Hall-resistivity would rise in small steps where the inverse of each plateau was an integer multiple of a combination of constants of nature. A few years later probes of gallium-arsenide, investigated under similar conditions, showed additional plateaus that would correspond to fractional multiples. These discoveries gave a completely new insight into the quantum mechanical processes that take place in flat semiconductor devices, and both were awarded with the Nobel prize in Physics: in 1985 the Nobel prize was given to Klaus von Klitzing, in 1998 to Robert Laughlin, Horst Störner and Daniel Tsui.

The FQH effect is a fascinating phenomenon and explained by theoreticians as being caused by one or more electrons forming composite states with the magnetic flux quanta. However, detailed experimental investigations of FQH are difficult to do in solids, and the states are very fragile. A cleaner implementation could be obtained by realizing the phenomenon in optical lattices in which ultracold atoms play the role of the electrons. This, and the hope to find simpler and more robust models displaying the FQH, is why theoreticians around the world seek to understand which mechanisms could lead to the observation of the FQH in lattices.

To this end the MPQ-team sets the focus on the topological properties that FQH states have. The topology of an object represents certain features of its geometrical structure: For example, a tee cup with a single hole in the handle and a bagel are topologically equivalent, because one can be transformed into the other without cutting it or punching holes in it. A bagel and a soccer ball, on the other hand, are not. In solid state systems the electrons experience the electric forces of many ions that are arranged in a periodic structure. Usually their energy levels make up straight and continuous energy ‘bands’ with a trivial topology. Instead, in systems that exhibit the fractional quantum Hall effect, the topology provides the material with exotic properties, like that the current can only be transmitted at the edge and is very robust against perturbations.

“We have developed a new lattice model where a FQH state should be observed,” Anne Nielsen says, first author of the publication. “It is defined on a two-dimensional lattice in which each site is occupied with a particle. Each particle can be either in a ‘spin up’ or a ‘spin down’ state. In addition, we imply specific, local, short range interactions between the particles.” (See figure 1.) Numerical investigations of the properties of this system showed that its topological behaviour is in accordance with the one expected for a FQH state. The system does, for example, possess long range correlations that lead to the presence of two different ground states of the system when considering periodic boundary conditions.

To obtain their model the researchers used some specific mathematical tools. These tools are by themselves interesting because they may be more widely applicable and thereby open up doors to construct further interesting models.

“The mechanism that leads to FQH in our model seems to be different from those in previous models”, Anne Nielsen points out. “And, furthermore, we have demonstrated how this model can be implemented with ultracold atoms in optical lattices. Realizing FQH states in optical lattices would give unique possibilities for detailed experimental investigations of the states under particularly well-controlled conditions and would, in addition, be a hallmark for quantum simulations.” Olivia Meyer-Streng

Figure 1: Illustration of the lattice model where each particle is either in a ‘spin up’ or a ‘spin down’ state. (Graphic: Anne Nielsen, MPQ)

Original publication:
Anne E. B. Nielsen, Germán Sierra, and J. Ignacio Cirac
Local models of fractional quantum Hall states in lattices and physical implementation

Nature Communications, 28 November 2013, DOI: 10.1038/ncomms3864

Contact:
Prof. Dr. J. Ignacio Cirac
Honorary Professor, TU München
Director at the Max-Planck-Institute of Quantum Optics
Phone: +49 (0)89 / 32 905 -705/736 /Fax: -336
E-mail: ignacio.cirac@mpq.mpg.de
Dr. Anne Nielsen
Max-Planck-Institute of Quantum Optics
Hans-Kopfermann-Straße 1
85748 Garching, Germany
Phone: +49 (0)89 / 32 905 -130 /Fax: -336
E-mail: anne.nielsen@mpq.mpg.de
Dr. Olivia Meyer-Streng
Press & Public Relations
Max-Planck-Institute of Quantum Optics
85748 Garching, Germany
Phone: +49 (0)89 / 32 905 -213
E-mail: olivia.meyer-streng@mpq.mpg.de

Dr. Olivia Meyer-Streng | Max-Planck-Institut
Further information:
http://www.mpq.mpg.de

More articles from Physics and Astronomy:

nachricht Computer model predicts how fracturing metallic glass releases energy at the atomic level
20.07.2018 | American Institute of Physics

nachricht What happens when we heat the atomic lattice of a magnet all of a sudden?
18.07.2018 | Forschungsverbund Berlin

All articles from Physics and Astronomy >>>

The most recent press releases about innovation >>>

Die letzten 5 Focus-News des innovations-reports im Überblick:

Im Focus: Future electronic components to be printed like newspapers

A new manufacturing technique uses a process similar to newspaper printing to form smoother and more flexible metals for making ultrafast electronic devices.

The low-cost process, developed by Purdue University researchers, combines tools already used in industry for manufacturing metals on a large scale, but uses...

Im Focus: First evidence on the source of extragalactic particles

For the first time ever, scientists have determined the cosmic origin of highest-energy neutrinos. A research group led by IceCube scientist Elisa Resconi, spokesperson of the Collaborative Research Center SFB1258 at the Technical University of Munich (TUM), provides an important piece of evidence that the particles detected by the IceCube neutrino telescope at the South Pole originate from a galaxy four billion light-years away from Earth.

To rule out other origins with certainty, the team led by neutrino physicist Elisa Resconi from the Technical University of Munich and multi-wavelength...

Im Focus: Magnetic vortices: Two independent magnetic skyrmion phases discovered in a single material

For the first time a team of researchers have discovered two different phases of magnetic skyrmions in a single material. Physicists of the Technical Universities of Munich and Dresden and the University of Cologne can now better study and understand the properties of these magnetic structures, which are important for both basic research and applications.

Whirlpools are an everyday experience in a bath tub: When the water is drained a circular vortex is formed. Typically, such whirls are rather stable. Similar...

Im Focus: Breaking the bond: To take part or not?

Physicists working with Roland Wester at the University of Innsbruck have investigated if and how chemical reactions can be influenced by targeted vibrational excitation of the reactants. They were able to demonstrate that excitation with a laser beam does not affect the efficiency of a chemical exchange reaction and that the excited molecular group acts only as a spectator in the reaction.

A frequently used reaction in organic chemistry is nucleophilic substitution. It plays, for example, an important role in in the synthesis of new chemical...

Im Focus: New 2D Spectroscopy Methods

Optical spectroscopy allows investigating the energy structure and dynamic properties of complex quantum systems. Researchers from the University of Würzburg present two new approaches of coherent two-dimensional spectroscopy.

"Put an excitation into the system and observe how it evolves." According to physicist Professor Tobias Brixner, this is the credo of optical spectroscopy....

All Focus news of the innovation-report >>>

Anzeige

Anzeige

VideoLinks
Industry & Economy
Event News

Leading experts in Diabetes, Metabolism and Biomedical Engineering discuss Precision Medicine

13.07.2018 | Event News

Conference on Laser Polishing – LaP: Fine Tuning for Surfaces

12.07.2018 | Event News

11th European Wood-based Panel Symposium 2018: Meeting point for the wood-based materials industry

03.07.2018 | Event News

 
Latest News

A smart safe rechargeable zinc ion battery based on sol-gel transition electrolytes

20.07.2018 | Power and Electrical Engineering

Reversing cause and effect is no trouble for quantum computers

20.07.2018 | Information Technology

Princeton-UPenn research team finds physics treasure hidden in a wallpaper pattern

20.07.2018 | Materials Sciences

VideoLinks
Science & Research
Overview of more VideoLinks >>>