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 A tale of two pulsars' tails: Plumes offer geometry lessons to astronomers
18.01.2017 | Penn State

nachricht Studying fundamental particles in materials
17.01.2017 | Max-Planck-Institut für Struktur und Dynamik der Materie

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: How gut bacteria can make us ill

HZI researchers decipher infection mechanisms of Yersinia and immune responses of the host

Yersiniae cause severe intestinal infections. Studies using Yersinia pseudotuberculosis as a model organism aim to elucidate the infection mechanisms of these...

Im Focus: Interfacial Superconductivity: Magnetic and superconducting order revealed simultaneously

Researchers from the University of Hamburg in Germany, in collaboration with colleagues from the University of Aarhus in Denmark, have synthesized a new superconducting material by growing a few layers of an antiferromagnetic transition-metal chalcogenide on a bismuth-based topological insulator, both being non-superconducting materials.

While superconductivity and magnetism are generally believed to be mutually exclusive, surprisingly, in this new material, superconducting correlations...

Im Focus: Studying fundamental particles in materials

Laser-driving of semimetals allows creating novel quasiparticle states within condensed matter systems and switching between different states on ultrafast time scales

Studying properties of fundamental particles in condensed matter systems is a promising approach to quantum field theory. Quasiparticles offer the opportunity...

Im Focus: Designing Architecture with Solar Building Envelopes

Among the general public, solar thermal energy is currently associated with dark blue, rectangular collectors on building roofs. Technologies are needed for aesthetically high quality architecture which offer the architect more room for manoeuvre when it comes to low- and plus-energy buildings. With the “ArKol” project, researchers at Fraunhofer ISE together with partners are currently developing two façade collectors for solar thermal energy generation, which permit a high degree of design flexibility: a strip collector for opaque façade sections and a solar thermal blind for transparent sections. The current state of the two developments will be presented at the BAU 2017 trade fair.

As part of the “ArKol – development of architecturally highly integrated façade collectors with heat pipes” project, Fraunhofer ISE together with its partners...

Im Focus: How to inflate a hardened concrete shell with a weight of 80 t

At TU Wien, an alternative for resource intensive formwork for the construction of concrete domes was developed. It is now used in a test dome for the Austrian Federal Railways Infrastructure (ÖBB Infrastruktur).

Concrete shells are efficient structures, but not very resource efficient. The formwork for the construction of concrete domes alone requires a high amount of...

All Focus news of the innovation-report >>>

Anzeige

Anzeige

Event News

12V, 48V, high-voltage – trends in E/E automotive architecture

10.01.2017 | Event News

2nd Conference on Non-Textual Information on 10 and 11 May 2017 in Hannover

09.01.2017 | Event News

Nothing will happen without batteries making it happen!

05.01.2017 | Event News

 
Latest News

A big nano boost for solar cells

18.01.2017 | Power and Electrical Engineering

Glass's off-kilter harmonies

18.01.2017 | Materials Sciences

Toward a 'smart' patch that automatically delivers insulin when needed

18.01.2017 | Life Sciences

VideoLinks
B2B-VideoLinks
More VideoLinks >>>