Forum for Science, Industry and Business

Sponsored by:     3M 
Search our Site:

 

Magic numbers of quantum matter revealed by cold atoms

08.01.2015

Scientists extract the topological number of an artificial solid subjected to extreme effective magnetic fields

Topology, a branch of mathematics classifying geometric objects, has been exploited by physicists to predict and describe unusual quantum phases: the topological states of matter. These intriguing phases, generally accessible at very low temperature, exhibit unique conductivity properties which are particularly robust against external perturbations, suggesting promising technological applications.


Fig. 1: The classification of geometric objects and quantum matter.

Chair of Quantum Optics, LMU


Fig. 2: The Chern-number measurement using an external force.

Chair of Quantum Optics, LMU

The great stability of topological states relies on a set of magic integers, the so-called Chern numbers, which remain immune to defects and deformations. For the first time, an international team of scientists succeeded to measure the topological Chern number in a non-electronic system with high precision.

The experiments were carried out with ultracold bosonic atoms controlled by lasers, in the group of Professor Immanuel Bloch (Ludwig-Maximilians-Universität Munich and Max Planck Institute of Quantum Optics, Garching) in collaboration with Nathan Goldman and Sylvain Nascimbène from the Collège de France and Nigel Cooper from Cambridge University.

Matter forms remarkable phases when it is immersed in extreme environments, such as strong magnetic fields and low temperature. Under these conditions, materials can reach unusual regimes where their electrical properties present universal and exotic behaviours, e.g. dissipationless currents and quantized electrical resistance. This physical framework sets the stage for new phases of matter, the topological states, which are described by magic (topological) integers.

They are mathematical numbers used to classify geometric objects [e.g. the number of holes in a surface, Fig. 1a], and which remain immune to deformations. The outstanding fact that quantum states of matter can be associated with topological numbers guarantees the robustness of their unique electrical properties against perturbations. This suggests numerous promising technological applications, e.g. in spintronics and quantum computation, hence motivating the search for novel topological states of matter in laboratories.

Topological states were discovered in the context of the quantum Hall effect, i.e. through studies of the electrical resistance in materials subjected to strong magnetic fields. After reaching sufficiently low temperatures, the measured resistance was found to form robust plateaus when varying the magnetic field, a behaviour which was shown to be independent of the sample.

Surprisingly, this universal physical property - the quantum Hall effect celebrated by the Nobel prize in 1985 - appeared to be rooted in topology: each resistance plateau is dictated by a topological number, the Chern number. "The beauty of this result relies in the fact that these magic mathematical numbers appear as intrinsic properties of the electrons moving in the material; it is intriguing that these abstract numbers actually lead to extraordinary observable phenomena", says theorist Nathan Goldman.

An interesting route for the search of topological phases of matter is offered by synthetic materials, which consist of ultracold atomic gases controlled by light. In these highly versatile experiments, neutral atoms are trapped in a periodic landscape created by standing waves of lasers. Cold atoms moving in these optical lattices have proven to be very well suited to mimic the dynamics of electrons propagating in real materials. However, in contrast to electrons, cold atoms are charge neutral; hence, they do not exhibit the Hall effect in the presence of a magnetic field. To overcome this limitation, new experimental techniques were developed in Munich in order to engineer effective magnetic fields for neutral atoms. In such arrangements, cold atoms behave as charged particles subjected to strong magnetic fields, offering a new platform to study the Hall effect and topological phases in a highly controllable and clean environment.

The optical-lattice setup realized in the Munich experiment has been specifically tailored so as to exhibit topological properties (Fig. 1b). Indeed, when inducing an effective magnetic field in the lattice, the atomic gas is characterized by a non-zero topological Chern number νch = 1. Nathan Goldman explains: "In this configuration, and in direct analogy with the electric Hall effect, the atomic cloud is expected to experience a characteristic transverse motion in response to an applied force (Fig. 2). Moreover, our theory predicts that this transverse drift should be directly proportional to the topological Chern number (νch = 1)". The experimentalists applied a force to their optical-lattice setup and analyzed such a displacement by taking snap-shots of the cloud.

From this sequence of images, they determined an experimental value for the Chern number νexp = 0.99(5) in excellent agreement with theory. This result constitutes the first Chern-number measurement in a non-electronic system. In contrast to electronic measurements, which are based on currents flowing along the edges of the sample, the Munich Chern-number measurement directly probes the topological nature of the bulk.

These measurements constitute an important step towards the realization and detection of topological states with ultracold atoms. Including interactions between the atoms could generate novel and exciting phases, such as the much sought after fractional Chern insulators. [N.G. and M.A.]

Figure captions:

Fig. 1: The classification of geometric objects and quantum matter. a. Topology classifies these three objects in terms of the number of handles g. The doughnut is equivalent to a mug (g=1), but differs from a ball (g=0). b. Illustration of an atomic gas trapped in a two-dimensional optical lattice: (left panel) a conventional lattice, and (right panel) a lattice subjected to an effective magnetic field. The related quantum phases are associated with different topological (Chern) numbers, schematically illustrated by the ball and the doughnut, respectively.

Fig. 2: The Chern-number measurement using an external force. a. The atoms are not deflected in a conventional lattice with zero Chern number. b. When the Chern number is νch = 1, the atoms are deflected transverse to the force.

Original publication:
M. Aidelsburger, M. Lohse, C. Schweizer, M. Atala, J. T. Barreiro, S. Nascimb ene, N. R. Cooper, I. Bloch & N. Goldman
Measuring the Chern number of Hofstadter bands with ultracold bosonic atoms
Nature Physics, 22 December 2014, Advance Online Publication, DOI:10.1038/nphys3171

Contact:
Prof. Dr. Immanuel Bloch
Chair of Quantum Optics, LMU München
Schellingstr. 4, 80799 Munich
Director at Max Planck Institute of Quantum Optics
Hans-Kopfermann-Str. 1, 85748 Garching, Germany
Phone: +49 (0)89 / 32 905 -138
E-mail: immanuel.bloch@mpq.mpg.de

Prof. Dr. Nathan Goldman
Collège de France, Laboratoire Kastler Brossel
11, place Marcelin Berthelot
75005 Paris, France, and
Center for Nonlinear Phenomena and Complex Systems,
Université Libre de Bruxelles, CP 231, Campus Plaine,
B-1050 Brussels, Belgium
Phone: +32 2 6505797
E-mail: nathan.goldman@lkb.ens.fr und ngoldman@ulb.ac.be

M. Sc. Monika Aidelsburger
LMU München, Faculty of Physics
Schellingstr. 4, 80799 Munich
Phone: +49 (0)89 / 21 80 -6119
E-mail: monika.aidelsburger@physik.uni-muenchen.de

Weitere Informationen:

http://www.mpq.mpg.de
http://www.quantum-munich.de

Dr. Olivia Meyer-Streng | Max-Planck-Institut für Quantenoptik

More articles from Physics and Astronomy:

nachricht Tracing aromatic molecules in the early universe
23.03.2017 | University of California - Riverside

nachricht New study maps space dust in 3-D
23.03.2017 | DOE/Lawrence Berkeley National Laboratory

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: Giant Magnetic Fields in the Universe

Astronomers from Bonn and Tautenburg in Thuringia (Germany) used the 100-m radio telescope at Effelsberg to observe several galaxy clusters. At the edges of these large accumulations of dark matter, stellar systems (galaxies), hot gas, and charged particles, they found magnetic fields that are exceptionally ordered over distances of many million light years. This makes them the most extended magnetic fields in the universe known so far.

The results will be published on March 22 in the journal „Astronomy & Astrophysics“.

Galaxy clusters are the largest gravitationally bound structures in the universe. With a typical extent of about 10 million light years, i.e. 100 times the...

Im Focus: Tracing down linear ubiquitination

Researchers at the Goethe University Frankfurt, together with partners from the University of Tübingen in Germany and Queen Mary University as well as Francis Crick Institute from London (UK) have developed a novel technology to decipher the secret ubiquitin code.

Ubiquitin is a small protein that can be linked to other cellular proteins, thereby controlling and modulating their functions. The attachment occurs in many...

Im Focus: Perovskite edges can be tuned for optoelectronic performance

Layered 2D material improves efficiency for solar cells and LEDs

In the eternal search for next generation high-efficiency solar cells and LEDs, scientists at Los Alamos National Laboratory and their partners are creating...

Im Focus: Polymer-coated silicon nanosheets as alternative to graphene: A perfect team for nanoelectronics

Silicon nanosheets are thin, two-dimensional layers with exceptional optoelectronic properties very similar to those of graphene. Albeit, the nanosheets are less stable. Now researchers at the Technical University of Munich (TUM) have, for the first time ever, produced a composite material combining silicon nanosheets and a polymer that is both UV-resistant and easy to process. This brings the scientists a significant step closer to industrial applications like flexible displays and photosensors.

Silicon nanosheets are thin, two-dimensional layers with exceptional optoelectronic properties very similar to those of graphene. Albeit, the nanosheets are...

Im Focus: Researchers Imitate Molecular Crowding in Cells

Enzymes behave differently in a test tube compared with the molecular scrum of a living cell. Chemists from the University of Basel have now been able to simulate these confined natural conditions in artificial vesicles for the first time. As reported in the academic journal Small, the results are offering better insight into the development of nanoreactors and artificial organelles.

Enzymes behave differently in a test tube compared with the molecular scrum of a living cell. Chemists from the University of Basel have now been able to...

All Focus news of the innovation-report >>>

Anzeige

Anzeige

Event News

International Land Use Symposium ILUS 2017: Call for Abstracts and Registration open

20.03.2017 | Event News

CONNECT 2017: International congress on connective tissue

14.03.2017 | Event News

ICTM Conference: Turbine Construction between Big Data and Additive Manufacturing

07.03.2017 | Event News

 
Latest News

When Air is in Short Supply - Shedding light on plant stress reactions when oxygen runs short

23.03.2017 | Life Sciences

Researchers use light to remotely control curvature of plastics

23.03.2017 | Power and Electrical Engineering

Sea ice extent sinks to record lows at both poles

23.03.2017 | Earth Sciences

VideoLinks
B2B-VideoLinks
More VideoLinks >>>