The properties of a hypothetical 4D material have been simulated in experiments done by two international teams of physicists. One team used light to emulate the 4D quantum Hall effect (QHE) while the other did it with ultracold atoms.
The quantum Hall effect has been the subject of several Nobel prizes and occurs in very thin conducting layers that are essentially 2D in nature. When such materials are cooled to near absolute zero and subject to a strong magnetic field, the electrical conductance is quantized and can change only in discrete steps. The QHE is a universal property of 2D conductors and can be seen in a wide range of materials – even when the samples are disordered.
While the QHE does not occur in 3D materials, in 2001 physicists predicted that it could also occur in systems with four spatial dimensions. But nature only has three spatial dimensions, so the idea of the 4D QHE had been a theoretical novelty – until now.
Mikael Rechtsman of Pennsylvania State University and colleagues built their 4D QHE system from an array of optical waveguides. The waveguides are closely-spaced tubes that are etched through a single piece of glass using a powerful laser (see figure). By carefully positioning the waveguides in the array, the team created extra “synthetic dimensions” that emulate a 4D material.
Current of light
In their system, light played the role of electrical current and the team showed that its transmission though the lattice was much like what occurs in a 4D QHE.
Meanwhile at the Max Planck Institute for Quantum Optics in Munich, Immanuel Bloch and colleagues created similar synthetic dimensions using a 2D array of ultracold atoms trapped by crisscrossing laser beams. Bloch’s team began with a regular square array of atoms. Then they applied additional laser beams in the plane of the array that were offset from the array’s symmetry axes. This created a complicated superlattice in which the atoms moved as described by the 4D QHE.
Both teams included Oded Zilberberg of ETH Zurich, who developed the theoretical basis for creating a 4D QHE in special 2D systems.
Rechtsman believes that the 4D QHE simulations are more than just esoteric curiosities and could have practical applications. He points out that quasicrystals – materials that are crystalline but have no repeating unit cells – can have “hidden dimensions”. Their structures, he says, “can be understood as projections from higher-dimensional space into the real, 3D world”, adding that this higher-dimensional physics could form the basis of new types of photonic devices.