Two independent groups of scientists have been able to reproduce four-dimensional properties of a quantum mechanical effect using a two-dimensional analog.
The two studies were published in Nature (here and here) and
focus on the quantum Hall effect. This effect describes how the conductance
(how well something transmits electricity) of a two-dimensional electron system
acts at a low temperature and in a strong magnetic field. It has been known for
a long time that this effect could also exist in a four-dimensional system, but
this has not been possible to prove until now.
"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, " Mikael Rechtsman, assistant
professor of physics and author of one of the papers, said in a statement.
"But, we have now shown that four-dimensional quantum Hall physics can be
emulated using photons – particles of light – flowing through an intricately
structured piece of glass – a waveguide array."
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The waveguide set-up used to test the 4D quantum Hall
effect. Rechtsman laboratory, Penn State University |
Thanks to a new technique, glass waveguides can be etched in
a way that makes them sport synthetic dimensions, allowing photons going
through the waveguides to act like they are in a true four-dimensional system.
This breakthrough allowed researchers to finally test if the quantum Hall
effect truly exists in four dimensions. And it does.
The effect cannot be observed in three dimensions. It was
first observed in two dimensions when electrical charges were sandwiched
between two surfaces. Once the surface cools to almost absolute zero and is
subjected to a strong magnetic field, the amount of charge that it can transmit
is quantized, fixed by the fundamental quantities of nature.
"Quantization is striking because even if the material
is 'messy' – that is, it has a lot of defects – this 'Hall conductance' remains
exceedingly stable," said Rechtsman. "This robustness of electron
flow – the quantum Hall effect – is universal and can be observed in many
different materials under very different conditions."
While there are no direct applications of four-dimensional
physics, the scientists think that a better understanding of the
four-dimensional quantum Hall effect could be used to develop new optical
systems, and maybe the use of higher dimensional waveguides could help explain
bizarre solids like quasicrystals.