JAN 05, 2018 11:30 AM PST

4-D Genie Out Of 2-D Bottle

WRITTEN BY: Daniel Duan

Illustration of light passing through a two-dimensional waveguide array. Credit: Rechtsman laboratory/PSU

According to a recently published study in Nature, an international team of researchers has demonstrated a way to observe physical phenomena known as quantum Hall effect, which was theorized to only exist in four-dimensional systems, in analogous real-world experiments.

If you find the last sentence confusing or mind-blogging, don't worry. The elaborate feat was indeed extraordinary because it was achieved with knowledges and efforts from three frontiers of physics: quantum mechanics, topology, and dimensionality.

Let us break down the news into a handful of chewable pieces. Hall effect refers to the production of a transverse electric field in a solid material, when the charged particles it carries move in a two-dimensional plane to an applied magnetic field perpendicular to the current. The magnetic field generates a Lorentz force, which deflects the particles in the direction orthogonal to their motion. This manifests in the appearance of a transverse voltage difference (Hall voltage).

Quantum Hall effect (or integer quantum Hall effect) is a quantum-mechanical version of the Hall effect. In 1980, Klaus von Klitzing made a remarkable observation: at a low temperature close to 4 Kelvin and powerful magnetic fields (in the order of 15 teslas), the hall voltage in two-dimensional electron systems can be quantized. (Being quantized means a characteristic is fixed to a fundamental constant of nature and cannot change.) He received 1985 Nobel Physics prize for this discovery.

In modern physics, string theory, a framework that tries to reconcile Einstein's ideas with the laws of quantum mechanics, postulates that there are up to 10 dimensions in our universe, contradicting the commonly accepted 3 (spatial) + 1 (temporal) dimension model. But of course, the unknown spatial dimensions only exist in the microscopic, subatomic realm, which quantum mechanics is supposed to take full control of.

How can one create a two-dimensional electron system? When an electric charge is sandwiched between two surfaces, the charge behaves effectively like a two-dimensional material, meaning its mobility is restricted to become linear. Since its discovery, the quantum Hall effect was not expected to exist in the higher-dimensional material. But in 2000, it was shown theoretically that a similar quantization could be observed in four-dimensional space.

To be clear, physicists cannot (at least not yet) create or access the 4th-dimension in reality. However, they can model this four-dimensional space using the so-called waveguide arrays. Within the arrays, each waveguide acts as a tube or conduit for photons. The collection of tubes is inscribed closely spaced through the high-quality glass, using a powerful laser.

In the study, to emulate a four-dimensional system, the researchers encoded two "synthetic dimensions" into the positions of the waveguides—the intricate patterns of the waveguide positions as a manifestation of the higher-dimensional coordinates. The researchers then measured how light flowed through the device and found that it behaved precisely according to the predictions of the four-dimensional quantum Hall effect.

"When it was theorized that the quantum Hall effect could be observed in four-dimensional space, it was considered to be of purely theoretical interest because the real world consists of only three spatial dimensions; it was more or less a curiosity,” said Mikael Rechtsman, professor of physics at the Pennsylvania State University and an author of the paper. His team has shown that four-dimensional quantum Hall physics can be emulated using photons—particles of light—flowing through a waveguide array. Rechtsman said: "Our observations, taken together with the observations using ultracold atoms, provide the first demonstration of higher-dimensional quantum Hall physics."

How can the higher-dimensional physics benefit science and technology in our normal-dimensional world? Quasicrystals—metallic alloys that are crystalline but have no repeating units and are used to coat some non-stick pans—have been shown to have “hidden dimensions”. Their structures can be seen as projections from higher-dimensional space into the real, three-dimensional world. Furthermore, insights into higher-dimensional physics can guide the design of novel computing and photonic devices.

Steven Girvin - Quantum Hall Effect. Credit: Institute of Quantum Computing

Source: phys.org

About the Author
  • Graduated with a bachelor degree in Pharmaceutical Science and a master degree in neuropharmacology, Daniel is a radiopharmaceutical and radiobiology expert based in Ottawa, Canada. With years of experience in biomedical R&D, Daniel is very into writing. He is constantly fascinated by what's happening in the world of science. He hopes to capture the public's interest and promote scientific literacy with his trending news articles. The recurring topics in his Chemistry & Physics trending news section include alternative energy, material science, theoretical physics, medical imaging, and green chemistry.
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