Researchers demonstrated a way to observe physical phenomena proposed to exist in higher-dimensional systems in analogous real-world experiments

In 2013, Oded Zilberberg and collaborators realized that key signatures of the 4D quantum Hall effect should also be visible in special time-dependent systems in two dimensions, so-called topological charge pumps, which constitute a dynamical version of the higher-dimensional model. This insight generalized an idea, which also goes back to David Thouless. In 1983, Thouless showed that a quantized transport of particles can be generated by periodically modulating a 1D system and that this response is mathematically equivalent to the 2D quantum Hall effect. Consequently, by combining two such systems in orthogonal directions, it should be possible to observe the non-linear Hall current predicted in 4D.

This has now been achieved by the group of Immanuel Bloch. At first a cloud of atoms is cooled down close to absolute zero and placed in a 2D optical lattice. Such an optical lattice is created by interference of retro-reflected laser beams of a certain wavelength along two orthogonal directions. The resulting potential resembles an egg-carton-like “crystal of light”, in which the atoms can move. By adding another laser beam with a different wavelength in each direction, a so-called superlattice is created. The researchers could implement the proposed 2D topological charge pump by introducing a constant tiny angle between the beams of different wavelength along one axis while at the same time dynamically changing the shape of the potential in the orthogonal direction by slightly shifting the wavelength of the additional laser beam.

When modulating the potential in time, the atoms predominantly move in the direction of the modulation and do so in a quantized way – the linear (i.e. 1D) response corresponding to the 2D quantum Hall effect as predicted by Thouless. But in addition to this, the Munich team also observed a slight drift in the transverse direction, even though the lattice potential in this direction remains static throughout the experiment. This transverse motion is the equivalent of the non-linear Hall response – the essential feature of the 4D Hall effect. By carefully monitoring and analyzing at which positions in the superlattice the atoms are located during this process, the scientists could furthermore demonstrate that this motion is quantized, thereby revealing the quantum nature of the Hall effect in 4D.

The results have now been published in the journal Nature together with complementary work by an American research team, which used photonic structures to study the intricate boundary phenomena that accompany this motion as a result of the 4D quantum Hall effect. Together, these papers provide the first experimental glimpse into the physics of higher-dimensional quantum Hall systems, which offer a number of fascinating future prospects. These include fundamental questions for our understanding of the universe like the interplay of quantum correlations and dimensionality, the generation of cosmic magnetic fields and quantum gravity, for which 4D quantum Hall systems have been proposed as toy models. [ML/OM]

SOURCE: Max Planck Institute of Quantum Optics

Prof. Dr. Immanuel Bloch
Chair of Quantum Optics
Ludwig-Maximilians-Universität München
Schellingstr. 4, 80799 Munich and
Director at the Max Planck Institute of Quantum Optics
Hans-Kopfermann-Str. 1
85748 Garching, Germany
Phone: +49 (0)89 / 32 905 -138
E-mail: immanuel.bloch@…

Dipl. Phys. Michael Lohse
LMU München
Schellingstr. 4, 80799 Munich
Phone: +49 (0)89 / 21 80 – 6133
E-mail: michael.lohse@…

Dr. Olivia Meyer-Streng
Press & Public Relations
Max Planck Institute of Quantum Optics, Garching, Germany
Phone: +49 (0)89 / 32 905 -213
E-mail: olivia.meyer-streng@…