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 Heating quantum matter: A novel view on topology
22.08.2017 | Université libre de Bruxelles

nachricht Engineering team images tiny quasicrystals as they form
18.08.2017 | Cornell University

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: Fizzy soda water could be key to clean manufacture of flat wonder material: Graphene

Whether you call it effervescent, fizzy, or sparkling, carbonated water is making a comeback as a beverage. Aside from quenching thirst, researchers at the University of Illinois at Urbana-Champaign have discovered a new use for these "bubbly" concoctions that will have major impact on the manufacturer of the world's thinnest, flattest, and one most useful materials -- graphene.

As graphene's popularity grows as an advanced "wonder" material, the speed and quality at which it can be manufactured will be paramount. With that in mind,...

Im Focus: Exotic quantum states made from light: Physicists create optical “wells” for a super-photon

Physicists at the University of Bonn have managed to create optical hollows and more complex patterns into which the light of a Bose-Einstein condensate flows. The creation of such highly low-loss structures for light is a prerequisite for complex light circuits, such as for quantum information processing for a new generation of computers. The researchers are now presenting their results in the journal Nature Photonics.

Light particles (photons) occur as tiny, indivisible portions. Many thousands of these light portions can be merged to form a single super-photon if they are...

Im Focus: Circular RNA linked to brain function

For the first time, scientists have shown that circular RNA is linked to brain function. When a RNA molecule called Cdr1as was deleted from the genome of mice, the animals had problems filtering out unnecessary information – like patients suffering from neuropsychiatric disorders.

While hundreds of circular RNAs (circRNAs) are abundant in mammalian brains, one big question has remained unanswered: What are they actually good for? In the...

Im Focus: RAVAN CubeSat measures Earth's outgoing energy

An experimental small satellite has successfully collected and delivered data on a key measurement for predicting changes in Earth's climate.

The Radiometer Assessment using Vertically Aligned Nanotubes (RAVAN) CubeSat was launched into low-Earth orbit on Nov. 11, 2016, in order to test new...

Im Focus: Scientists shine new light on the “other high temperature superconductor”

A study led by scientists of the Max Planck Institute for the Structure and Dynamics of Matter (MPSD) at the Center for Free-Electron Laser Science in Hamburg presents evidence of the coexistence of superconductivity and “charge-density-waves” in compounds of the poorly-studied family of bismuthates. This observation opens up new perspectives for a deeper understanding of the phenomenon of high-temperature superconductivity, a topic which is at the core of condensed matter research since more than 30 years. The paper by Nicoletti et al has been published in the PNAS.

Since the beginning of the 20th century, superconductivity had been observed in some metals at temperatures only a few degrees above the absolute zero (minus...

All Focus news of the innovation-report >>>

Anzeige

Anzeige

Event News

Call for Papers – ICNFT 2018, 5th International Conference on New Forming Technology

16.08.2017 | Event News

Sustainability is the business model of tomorrow

04.08.2017 | Event News

Clash of Realities 2017: Registration now open. International Conference at TH Köln

26.07.2017 | Event News

 
Latest News

Cholesterol-lowering drugs may fight infectious disease

22.08.2017 | Health and Medicine

Meter-sized single-crystal graphene growth becomes possible

22.08.2017 | Materials Sciences

Repairing damaged hearts with self-healing heart cells

22.08.2017 | Life Sciences

VideoLinks
B2B-VideoLinks
More VideoLinks >>>