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Report

Teaser, summary, work performed and final results

Periodic Reporting for period 2 - Quasicrystal (An Optical Quasicrystal for ultracold atoms)

Teaser

Summary

During the last twenty years, ultracold atoms in optical lattices have emerged as powerful quantum simulators for the physics of interacting electrons in solids. They have e.g. been used to study effects of strong correlations (Mott insulators), disorder and topology. In more than one dimension, these studies have mostly been restricted to periodic potentials, such as those in regular crystals.
In condensed matter systems, however, there exist also alternatives to simple periodic crystals. Quasicrystals are a novel form of condensed matter that is non-periodic, but long-range ordered. They have first been observed in the 1980s by Dan Shechtman in diffraction experiments. Quasicrystals give rise to a pattern of sharp Bragg peaks, similar to periodic crystals, but with rotational symmetries that are impossible for periodic structures. Their structure was found to be given by aperiodic tilings with more than one unit cell, such as the celebrated Penrose tiling.
Even though quasicrystals are long-range ordered, many foundational concepts of periodic condensed matter systems such as Blochwaves or Brillouin zones are not applicable. This places them on an interesting middle ground between periodic and disordered systems and highlights their potential for novel many-body physics.
The main objective of this proposal has been to extend the level of control provided by optical lattices to quasiperiodic potentials by realizing an optical quasicrystal.

Quasicrystals were also found to be responsible for the strength of high-strength steel and have even been used as non-stick coatings. Due to their unique properties, quasicrystals are by now also being considered as potential hydrogen storage materials, thermal barriers, and infrared sensors. They exhibit interesting friction properties and are considered as catalysts for chemical reactions. It is therefore im portnat to develop a better understanding of their electronic properties in order to capitalise on their unique properties. Furthermore, quasicrystalline structures have been realized in optical metamaterials and can potentially be used as superstructures in other materials.

Work performed

The main objective of this proposal has been to extend the level of control provided by optical lattices to quasiperiodic potentials by realizing an optical quasicrystal. We have been successful and could in 2019 present first diffraction experiments that demonstrate the high rotational symmetry and explore the resulting fractal structure in momentum space. In addition, we showed that these systems can also be understood as lattices in higher dimensions, i.e. we could realize two synthetic dimensions. Contrary to typical realizations of synthetic dimensions, in this approach the synthetic dimensions are unconstraint.We furthermore studied the tight-binding limits of these systems theoretically and numerically and found new and unexpected localisation properties, such as non-power-law critical properties and mixed spectra, where extended and localised states coexist at the same energy.

Final results

In the remaining part of the project, we will extend out investigations to strongly interacting systems. We will investigate the fate of the Mott transition in the quasiperiodic case and aim to map out the ground state phase diagram including the 2D Bose glass. We furthermore plan to realize the slightly controversial 2D Many-body localisation (MBL) transition â€“ we have theoretical evidence that the main potential obstacle to 2D MBL, namely rare thermal regions in the disorder potential, are absent in suitable quasiperiodic potentials. Another direction that we have just started to explore is the topology of this system, where we hope to observe topologically protected edge states.