To the best of our knowledge, we humans can only experience this world in three spatial dimensions (plus one time dimension): up and down, left and right, and forward and backward. But in two physics labs, scientists have found a way to represent a fourth spatial dimension.

This isn’t a fourth dimension that you can disappear into or anything like that. Instead, two teams of physicists engineered special two-dimensional setups, one with ultra-cold atoms and another with light particles. Both cases demonstrated different but complementary outcomes that looked the same as something called the “quantum Hall effect” occurring in four dimensions. These experiments could have important implications to fundamental science, or even allow engineers to access higher-dimension physics in our lower-dimension world.

“Physically, we don’t have a 4D spatial system, but we can access 4D quantum Hall physics using this lower-dimensional system because the higher-dimensional system is coded in the complexity of the structure,” Mikael Rechtsman, professor at Penn State University behind one of the papers, told Gizmodo. “Maybe we can come up with new physics in the higher dimension and then design devices that take advantage the higher-dimensional physics in lower dimensions.”

For the first time, physicists have built a two-dimensional experimental system that allows them to study the physical properties of materials that were theorized to exist only in four-dimensional space. An international team of researchers from Penn State, ETH Zurich in Switzerland, the University of Pittsburgh, and the Holon Institute of Technology in Israel have demonstrated that the behavior of particles of light can be made to match predictions about the four-dimensional version of the “quantum Hall effect”—a phenomenon that has been at the root of three Nobel Prizes in physics—in a two-dimensional array of “waveguides.”

A paper describing the research appears January 4, 2018 in the journal Nature along with a paper from a separate group from Germany that shows that a similar mechanism can be used to make a gas of ultracold atoms exhibit four-dimensional quantum Hall physics as well.

“When it was theorized that the quantum Hall effect could be observed in four-dimensional space,” said Mikael Rechtsman, assistant professor of physics and an author of the paper, “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. 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.”

A cylindrical rod is rotationally symmetric — after any arbitrary rotation around its axis it always looks the same. If an increasingly large force is applied to it in the longitudinal direction, however, it will eventually buckle and lose its rotational symmetry. Such processes, known as “spontaneous symmetry breaking”, also occur in subtle ways in the microscopic quantum world, where they are responsible for a number of fundamental phenomena such as magnetism and superconductivity. A team of researchers led by ETH professor Tilman Esslinger and Senior Scientist Tobias Donner at the Institute for Quantum Electronics has now studied the consequences of spontaneous symmetry breaking in detail using a quantum simulator. The results of their research have recently been published in the scientific journal Science.

Phase transitions caused by symmetry breaking

In their new work, Esslinger and his collaborators took a particular interest in phase transitions — physical processes, that is, in which the properties of a material change drastically, such as the transition of a material from solid to liquid or the spontaneous magnetization of a solid. In a particular type of phase transition that is caused by spontaneous symmetry breaking, so-called Higgs and Goldstone modes appear. Those modes describe how the particles in a material react collectively to a perturbation from the outside. “Such collective excitations have only been detected indirectly so far,” explains Julian Léonard, who obtained his doctorate in Esslinger’s laboratory now works as a post-doc at Harvard University, “but now we have succeeded in directly observing the character of those modes, which is dictated by symmetry.”