Scientists have demonstrated the ability to measure the impact of physical phenomena in four dimensions on experiments in a three-dimensional world. The new work builds on the discoveries that were awarded the Nobel Prize in Physics for 2016 and can form the basis of fundamentally new approaches to understanding quantum mechanics, as well as building a theory of quantum gravity. An article by the European team was published in the journal Nature.
The world around us appears to have three dimensions. However, many physical theories consider situations with a large number of dimensions: in general relativity there are four of them (three spatial and one temporal, combined into one continuum), and in superstring theory, only 10 independent spatial directions are considered. The new work of physicists shows the possibility of observing the influence of four-dimensional processes on three-dimensional experiments, which can be figuratively compared to the casting of a two-dimensional shadow by three-dimensional objects.
Physicists study a system of ultracold atoms in a two-dimensional optical trap of laser beams, which creates a superlattice - the superposition of two periodic potentials with different periods. In this design, a new type of quantum Hall effect appears, which is predicted for four-dimensional systems. The usual Hall effect occurs when charged particles move in a plane in the presence of a magnetic field. The field acts on the particles by the Lorentz force, which deflects them in a direction perpendicular to the motion. As a result, a transverse (relative to the original direction of motion) potential difference appears, called the Hall voltage. In 1980, Klaus von Klitzing showedthat at very low temperatures and high magnetic fields, this voltage can only take on certain values - this discovery is called the integer quantum Hall effect.
Later it turned out that the necessary condition for the appearance of the quantum Hall effect is precisely the two-dimensionality of the system, and its specific physical properties are not so important. This is due to the topology of the quantum mechanical wave function. It can also be proved that such an effect is impossible in three-dimensional bodies, since the direction perpendicular to the velocity is not uniquely determined.
Subsequent studies showed that in the case of four measurements, a similar effect should exist, for which a number of fundamentally new properties were predicted, for example, a nonlinear Hall current. For a long time, this remained a theoretical model without the possibility of verification in experiment. However, in 2013, physicists figured out that the four-dimensional Hall effect can be felt in a special two-dimensional system called topological charge pumps. This idea has only now been realized in a special two-dimensional optical superlattice. In it, beams of different wavelengths were directed along one direction at slightly different angles, and along the other, the shape of the optical potential was dynamically changed by shifting the wavelength of an additional laser.
As a result, atoms in such a trap move predominantly along a direction with an alternating potential, and in a quantum manner - this corresponds to the one-dimensional model of the two-dimensional Hall effect. However, at the same time, physicists discovered a gradual displacement in the transverse direction, although the potential along it remained constant throughout the experiment. This movement corresponds to a non-linear 4D Hall effect. Accurate measurements confirmed the quantum nature of the motion of atoms in this direction, which shows the quantum nature of the first demonstrated four-dimensional phenomenon.